<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2023-11-03T11:59:27.6122+00:00 -->
<!-- Copyright (c) 2023 Donnelly Financial Solutions, Inc. All Rights Reserved. -->
<xsd:schema targetNamespace="http://cccis.com/20230930" attributeFormDefault="unqualified" elementFormDefault="qualified" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2022-03-31" xmlns:country="http://xbrl.sec.gov/country/2023" xmlns:ecd-sub="http://xbrl.sec.gov/ecd-sub/2023" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:dei="http://xbrl.sec.gov/dei/2023" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:srt="http://fasb.org/srt/2023" xmlns:us-gaap="http://fasb.org/us-gaap/2023" xmlns:cccs="http://cccis.com/20230930" xmlns:xlink="http://www.w3.org/1999/xlink">
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/instance"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/linkbase"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd" namespace="http://xbrl.org/2005/xbrldt"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/dei/2023/dei-2023.xsd" namespace="http://xbrl.sec.gov/dei/2023"/>
  <xsd:import schemaLocation="https://www.xbrl.org/2020/extensible-enumerations-2.0.xsd" namespace="http://xbrl.org/2020/extensible-enumerations-2.0"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2023/ecd-sub-2023.xsd" namespace="http://xbrl.sec.gov/ecd-sub/2023"/>
  <xsd:import schemaLocation="https://www.xbrl.org/dtr/type/2022-03-31/types.xsd" namespace="http://www.xbrl.org/dtr/type/2022-03-31"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd" namespace="http://fasb.org/us-gaap/2023"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/country/2023/country-2023.xsd" namespace="http://xbrl.sec.gov/country/2023"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd" namespace="http://fasb.org/srt/2023"/>
  <xsd:annotation>
    <xsd:appinfo>
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cccs-20230930_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:title="Labels link" xlink:type="simple"/>
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cccs-20230930_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:title="Presentation link" xlink:type="simple"/>
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cccs-20230930_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:title="Definition link" xlink:type="simple"/>
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cccs-20230930_cal.xml" xlink:role="http://www.xbrl.org/2003/role/calculationLinkbaseRef" xlink:title="Calculation link" xlink:type="simple"/>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/CoverPage" id="CoverPage">
        <link:definition>100000 - Document - Cover Page</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/CondensedConsolidatedBalanceSheets" id="CondensedConsolidatedBalanceSheets">
        <link:definition>100010 - Statement - Condensed Consolidated Balance Sheets</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/CondensedConsolidatedBalanceSheetsParenthetical" id="CondensedConsolidatedBalanceSheetsParenthetical">
        <link:definition>100020 - Statement - Condensed Consolidated Balance Sheets (Parenthetical)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StatementCondensedConsolidatedStatementsOfOperationsAndComprehensiveLossIncomeUnaudited2" id="StatementCondensedConsolidatedStatementsOfOperationsAndComprehensiveLossIncomeUnaudited2">
        <link:definition>100030 - Statement - Condensed Consolidated Statements of Operations and Comprehensive (Loss) Income (Unaudited) 2</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StatementCondensedConsolidatedStatementsOfOperationsAndComprehensiveLossIncomeUnaudited" id="StatementCondensedConsolidatedStatementsOfOperationsAndComprehensiveLossIncomeUnaudited">
        <link:definition>100040 - Statement - Condensed Consolidated Statements of Operations and Comprehensive (Loss) Income (Unaudited)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/CondensedConsolidatedStatementsOfMezzanineEquityAndStockholdersEquity" id="CondensedConsolidatedStatementsOfMezzanineEquityAndStockholdersEquity">
        <link:definition>100050 - Statement - Condensed Consolidated Statements of Mezzanine Equity and Stockholders' Equity</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StatementCondensedConsolidatedStatementsOfCashFlowsUnaudited" id="StatementCondensedConsolidatedStatementsOfCashFlowsUnaudited">
        <link:definition>100060 - Statement - Condensed Consolidated Statements of Cash Flows (Unaudited)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/OrganizationAndNatureOfOperations" id="OrganizationAndNatureOfOperations">
        <link:definition>995455 - Disclosure - Organization and Nature of Operations</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SummaryOfSignificantAccountingPolicies" id="SummaryOfSignificantAccountingPolicies">
        <link:definition>995465 - Disclosure - Summary of Significant Accounting Policies</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureBusinessAcquisition" id="DisclosureBusinessAcquisition">
        <link:definition>995475 - Disclosure - Business Acquisition</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/Revenue" id="Revenue">
        <link:definition>995485 - Disclosure - Revenue</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/FairValueMeasurements" id="FairValueMeasurements">
        <link:definition>995495 - Disclosure - Fair Value Measurements</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/IncomeTaxes" id="IncomeTaxes">
        <link:definition>995505 - Disclosure - Income Taxes</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/AccountsReceivable" id="AccountsReceivable">
        <link:definition>995515 - Disclosure - Accounts Receivable</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/OtherCurrentAssets" id="OtherCurrentAssets">
        <link:definition>995525 - Disclosure - Other Current Assets</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SoftwareEquipmentAndProperty" id="SoftwareEquipmentAndProperty">
        <link:definition>995535 - Disclosure - Software, Equipment, And Property</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/Leases" id="Leases">
        <link:definition>995545 - Disclosure - Leases</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/GoodwillAndIntangibleAssets" id="GoodwillAndIntangibleAssets">
        <link:definition>995555 - Disclosure - Goodwill and Intangible Assets</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/AccruedExpenses" id="AccruedExpenses">
        <link:definition>995565 - Disclosure - Accrued Expenses</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/OtherLiabilities" id="OtherLiabilities">
        <link:definition>995575 - Disclosure - Other Liabilities</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LongTermDebt" id="LongTermDebt">
        <link:definition>995585 - Disclosure - Long-Term Debt</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LongTermLicensingAgreement" id="LongTermLicensingAgreement">
        <link:definition>995595 - Disclosure - Long-Term Licensing Agreement</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/RedeemableNonControllingInterest" id="RedeemableNonControllingInterest">
        <link:definition>995605 - Disclosure - Redeemable Non-Controlling Interest</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/CapitalStock" id="CapitalStock">
        <link:definition>995615 - Disclosure - Capital Stock</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/EmployeeBenefitPlans" id="EmployeeBenefitPlans">
        <link:definition>995625 - Disclosure - Employee Benefit Plans</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StockIncentivePlans" id="StockIncentivePlans">
        <link:definition>995635 - Disclosure - Stock Incentive Plans</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/Warrants" id="Warrants">
        <link:definition>995645 - Disclosure - Warrants</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/Commitments" id="Commitments">
        <link:definition>995655 - Disclosure - Commitments</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureLegalProceedingsAndContingencies" id="DisclosureLegalProceedingsAndContingencies">
        <link:definition>995665 - Disclosure - Legal Proceedings and Contingencies</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/RelatedParties" id="RelatedParties">
        <link:definition>995675 - Disclosure - Related Parties</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureNetLossIncomePerShare" id="DisclosureNetLossIncomePerShare">
        <link:definition>995685 - Disclosure - Net (Loss) Income Per Share</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SegmentInformationAndInformationAboutGeographicAreas" id="SegmentInformationAndInformationAboutGeographicAreas">
        <link:definition>995695 - Disclosure - Segment Information And Information About Geographic Areas</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/Divestiture" id="Divestiture">
        <link:definition>995705 - Disclosure - Divestiture</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureGainOnSaleOfCostMethodInvestment1" id="DisclosureGainOnSaleOfCostMethodInvestment1">
        <link:definition>995715 - Disclosure - Gain on Sale of Cost Method Investment</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SummaryOfSignificantAccountingPoliciesPolicies" id="SummaryOfSignificantAccountingPoliciesPolicies">
        <link:definition>995725 - Disclosure - Summary of Significant Accounting Policies (Policies)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureBusinessAcquisitionTables" id="DisclosureBusinessAcquisitionTables">
        <link:definition>995735 - Disclosure - Business Acquisition (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/RevenueTables" id="RevenueTables">
        <link:definition>995745 - Disclosure - Revenue (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/FairValueMeasurementsTables" id="FairValueMeasurementsTables">
        <link:definition>995755 - Disclosure - Fair Value Measurements (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/AccountsReceivableTables" id="AccountsReceivableTables">
        <link:definition>995765 - Disclosure - Accounts Receivable (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/OtherCurrentAssetsTables" id="OtherCurrentAssetsTables">
        <link:definition>995775 - Disclosure - Other Current Assets (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SoftwareEquipmentAndPropertyTables" id="SoftwareEquipmentAndPropertyTables">
        <link:definition>995785 - Disclosure - Software, Equipment, And Property (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LeasesTables" id="LeasesTables">
        <link:definition>995795 - Disclosure - Leases (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/GoodwillAndIntangibleAssetsTables" id="GoodwillAndIntangibleAssetsTables">
        <link:definition>995805 - Disclosure - Goodwill and Intangible Assets (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/AccruedExpensesTables" id="AccruedExpensesTables">
        <link:definition>995815 - Disclosure - Accrued Expenses (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/OtherLiabilitiesTables" id="OtherLiabilitiesTables">
        <link:definition>995825 - Disclosure - Other Liabilities (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LongTermDebtTables" id="LongTermDebtTables">
        <link:definition>995835 - Disclosure - Long-Term Debt (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRedeemableNoncontrollingInterestTables" id="DisclosureRedeemableNoncontrollingInterestTables">
        <link:definition>995845 - Disclosure - Redeemable Non-controlling Interest (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StockIncentivePlansTables" id="StockIncentivePlansTables">
        <link:definition>995855 - Disclosure - Stock Incentive Plans (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRelatedPartiesTables" id="DisclosureRelatedPartiesTables">
        <link:definition>995865 - Disclosure - Related Parties (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureNetLossIncomePerShareTables" id="DisclosureNetLossIncomePerShareTables">
        <link:definition>995875 - Disclosure - Net (Loss) Income Per Share (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SegmentInformationAndInformationAboutGeographicAreasTables" id="SegmentInformationAndInformationAboutGeographicAreasTables">
        <link:definition>995885 - Disclosure - Segment Information And Information About Geographic Areas (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureBusinessAcquisitionAdditionalInformationDetail" id="DisclosureBusinessAcquisitionAdditionalInformationDetail">
        <link:definition>995895 - Disclosure - Business Acquisition - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureBusinessAcquisitionScheduleOfBusinessAcquisitionByAcquisitionDetails" id="DisclosureBusinessAcquisitionScheduleOfBusinessAcquisitionByAcquisitionDetails">
        <link:definition>995905 - Disclosure - Business Acquisition - Schedule of Business Acquisition by Acquisition (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureBusinessAcquisitionScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedDetails" id="DisclosureBusinessAcquisitionScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedDetails">
        <link:definition>995915 - Disclosure - Business Acquisition - Schedule of Recognized Identified Assets Acquired and Liabilities Assumed (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRevenueSummarizesRevenueByTypeOfServiceDetails" id="DisclosureRevenueSummarizesRevenueByTypeOfServiceDetails">
        <link:definition>995925 - Disclosure - Revenue - Summarizes Revenue By Type of Service (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRevenueAdditionalInformationDetails" id="DisclosureRevenueAdditionalInformationDetails">
        <link:definition>995935 - Disclosure - Revenue - Additional Information (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRevenueSummaryOfReceivablesContractAssetsAndContractLiabilitiesFromContractsWithCustomersDetail" id="DisclosureRevenueSummaryOfReceivablesContractAssetsAndContractLiabilitiesFromContractsWithCustomersDetail">
        <link:definition>995945 - Disclosure - Revenue - Summary of Receivables Contract Assets and Contract Liabilities from Contracts with Customers (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRevenueSummaryOfDeferredRevenueDetail" id="DisclosureRevenueSummaryOfDeferredRevenueDetail">
        <link:definition>995955 - Disclosure - Revenue - Summary of Deferred Revenue (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRevenueSummaryOfDeferredContractCostsDetail" id="DisclosureRevenueSummaryOfDeferredContractCostsDetail">
        <link:definition>995965 - Disclosure - Revenue - Summary of Deferred Contract Costs (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/FairValueMeasurementsAdditionalInformationDetail" id="FairValueMeasurementsAdditionalInformationDetail">
        <link:definition>995975 - Disclosure - Fair Value Measurements - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureFairValueMeasurementsFairValueMeasurementInputsAndValuationTechniquesDetails" id="DisclosureFairValueMeasurementsFairValueMeasurementInputsAndValuationTechniquesDetails">
        <link:definition>995985 - Disclosure - Fair Value Measurements - Fair Value Measurement Inputs and Valuation Techniques (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/FairValueMeasurementsSummaryOfAssetsAndLiabilitiesMeasuredAtFairValueOnARecurringBasisDetail" id="FairValueMeasurementsSummaryOfAssetsAndLiabilitiesMeasuredAtFairValueOnARecurringBasisDetail">
        <link:definition>995995 - Disclosure - Fair Value Measurements - Summary of Assets and Liabilities Measured at Fair Value on a Recurring Basis (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/FairValueMeasurementsSummaryOfCarryingAmountsAndEstimatedFairValueOfTheFinancialInstrumentsDetail" id="FairValueMeasurementsSummaryOfCarryingAmountsAndEstimatedFairValueOfTheFinancialInstrumentsDetail">
        <link:definition>996005 - Disclosure - Fair Value Measurements - Summary of Carrying Amounts and Estimated Fair Value of the Financial Instruments (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/IncomeTaxesAdditionalInformationDetail" id="IncomeTaxesAdditionalInformationDetail">
        <link:definition>996015 - Disclosure - Income Taxes - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureAccountsReceivableAdditionalInformationDetail" id="DisclosureAccountsReceivableAdditionalInformationDetail">
        <link:definition>996025 - Disclosure - Accounts Receivable - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/AccountsReceivableScheduleOfAccountsReceivableNetDetail" id="AccountsReceivableScheduleOfAccountsReceivableNetDetail">
        <link:definition>996035 - Disclosure - Accounts Receivable - Schedule of Accounts Receivable, Net (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/AccountsReceivableScheduleOfChangesToTheAllowanceForDoubtfulAccountsAndSalesReservesDetail" id="AccountsReceivableScheduleOfChangesToTheAllowanceForDoubtfulAccountsAndSalesReservesDetail">
        <link:definition>996045 - Disclosure - Accounts Receivable - Schedule of Changes to the Allowance for Doubtful Accounts and Sales Reserves (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/OtherCurrentAssetsScheduleOfOtherCurrentAssetsDetail" id="OtherCurrentAssetsScheduleOfOtherCurrentAssetsDetail">
        <link:definition>996055 - Disclosure - Other Current Assets - Schedule of Other Current Assets (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SoftwareEquipmentAndPropertyScheduleOfSoftwareEquipmentAndPropertyDetail" id="SoftwareEquipmentAndPropertyScheduleOfSoftwareEquipmentAndPropertyDetail">
        <link:definition>996065 - Disclosure - Software, Equipment, And Property - Schedule of Software,Equipment and Property (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SoftwareEquipmentAndPropertyAdditionalInformationDetail" id="SoftwareEquipmentAndPropertyAdditionalInformationDetail">
        <link:definition>996075 - Disclosure - Software, Equipment, And Property - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LeasesAdditionalInformationDetail" id="LeasesAdditionalInformationDetail">
        <link:definition>996085 - Disclosure - Leases - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LeasesSummaryOfLeaseCostDetail" id="LeasesSummaryOfLeaseCostDetail">
        <link:definition>996095 - Disclosure - Leases - Summary of Lease Cost (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/GoodwillAndIntangibleAssetsAdditionalInformationDetail" id="GoodwillAndIntangibleAssetsAdditionalInformationDetail">
        <link:definition>996105 - Disclosure - Goodwill and Intangible Assets - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureGoodwillAndIntangibleAssetsScheduleOfGrossAmountAccumulatedImpairmentLossAndCarryingAmountOfGoodwillDetail" id="DisclosureGoodwillAndIntangibleAssetsScheduleOfGrossAmountAccumulatedImpairmentLossAndCarryingAmountOfGoodwillDetail">
        <link:definition>996115 - Disclosure - Goodwill and Intangible Assets - Schedule of Gross Amount, Accumulated Impairment Loss, and Carrying Amount of Goodwill (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureGoodwillAndIntangibleAssetsScheduleOfChangesInTheCarryingAmountOfGoodwillDetail" id="DisclosureGoodwillAndIntangibleAssetsScheduleOfChangesInTheCarryingAmountOfGoodwillDetail">
        <link:definition>996125 - Disclosure - Goodwill and Intangible Assets - Schedule of Changes in the Carrying Amount of Goodwill (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/GoodwillAndIntangibleAssetsSummaryOfIntangibleAssetsBalanceDetail" id="GoodwillAndIntangibleAssetsSummaryOfIntangibleAssetsBalanceDetail">
        <link:definition>996135 - Disclosure - Goodwill and Intangible Assets - Summary of Intangible Assets Balance (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/GoodwillAndIntangibleAssetsScheduleOfFutureAmortizationExpenseForIntangibleAssetsDetail" id="GoodwillAndIntangibleAssetsScheduleOfFutureAmortizationExpenseForIntangibleAssetsDetail">
        <link:definition>996145 - Disclosure - Goodwill and Intangible Assets - Schedule of Future Amortization Expense for Intangible Assets (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/AccruedExpensesScheduleOfAccruedExpensesDetail" id="AccruedExpensesScheduleOfAccruedExpensesDetail">
        <link:definition>996155 - Disclosure - Accrued Expenses - Schedule of Accrued Expenses (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/OtherLiabilitiesSummaryOfOtherLiabilitiesDetail" id="OtherLiabilitiesSummaryOfOtherLiabilitiesDetail">
        <link:definition>996165 - Disclosure - Other Liabilities - Summary of Other Liabilities (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LongTermDebtAdditionalInformationDetail" id="LongTermDebtAdditionalInformationDetail">
        <link:definition>996175 - Disclosure - Long-Term Debt - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/LongTermDebtSummaryOfLongTermDebtDetail" id="LongTermDebtSummaryOfLongTermDebtDetail">
        <link:definition>996185 - Disclosure - Long-Term Debt - Summary of Long Term Debt (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/RedeemableNonControllingInterestAdditionalInformationDetail" id="RedeemableNonControllingInterestAdditionalInformationDetail">
        <link:definition>996195 - Disclosure - Redeemable Non-Controlling Interest - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRedeemableNoncontrollingInterestScheduleOfActivitiesImpactingTheRedeemableNoncontrollableInterestDetail" id="DisclosureRedeemableNoncontrollingInterestScheduleOfActivitiesImpactingTheRedeemableNoncontrollableInterestDetail">
        <link:definition>996205 - Disclosure - Redeemable Non-controlling Interest - Schedule of activities impacting the redeemable non-controllable interest (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/CapitalStockAdditionalInformationDetail" id="CapitalStockAdditionalInformationDetail">
        <link:definition>996215 - Disclosure - Capital Stock - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/EmployeeBenefitPlansAdditionalInformationDetail" id="EmployeeBenefitPlansAdditionalInformationDetail">
        <link:definition>996225 - Disclosure - Employee Benefit Plans - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureStockIncentivePlansScheduleOfNonvestedRestrictedStockUnitsActivityDetails" id="DisclosureStockIncentivePlansScheduleOfNonvestedRestrictedStockUnitsActivityDetails">
        <link:definition>996235 - Disclosure - Stock Incentive Plans - Schedule of Non-vested Restricted Stock Units Activity (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StockIncentivePlansAdditionalInformationDetail" id="StockIncentivePlansAdditionalInformationDetail">
        <link:definition>996245 - Disclosure - Stock Incentive Plans - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StockIncentivePlansSummaryOfShareBasedCompensationArrangementsByShareBasedPaymentAwardDetail" id="StockIncentivePlansSummaryOfShareBasedCompensationArrangementsByShareBasedPaymentAwardDetail">
        <link:definition>996255 - Disclosure - Stock Incentive Plans - Summary of Share-based Compensation Arrangements by Share-based Payment Award (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureStockIncentivePlansScheduleOfSharebasedPaymentAwardStockOptionsValuationAssumptionsDetail" id="DisclosureStockIncentivePlansScheduleOfSharebasedPaymentAwardStockOptionsValuationAssumptionsDetail">
        <link:definition>996265 - Disclosure - Stock Incentive Plans - Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/StockIncentivePlansSummaryOfShareBasedPaymentArrangementExpensedAndCapitalizedAmountDetail" id="StockIncentivePlansSummaryOfShareBasedPaymentArrangementExpensedAndCapitalizedAmountDetail">
        <link:definition>996275 - Disclosure - Stock Incentive Plans - Summary of Share-based Payment Arrangement, Expensed and Capitalized, Amount (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/WarrantsAdditionalInformationDetail" id="WarrantsAdditionalInformationDetail">
        <link:definition>996285 - Disclosure - Warrants - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/CommitmentsAdditionalInformationDetail" id="CommitmentsAdditionalInformationDetail">
        <link:definition>996295 - Disclosure - Commitments - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureRelatedPartiesScheduleOfRevenuesExpensesAndAmountReceivableWithEntitiesAffiliatedWithPrincipalOwnersDetail" id="DisclosureRelatedPartiesScheduleOfRevenuesExpensesAndAmountReceivableWithEntitiesAffiliatedWithPrincipalOwnersDetail">
        <link:definition>996305 - Disclosure - Related Parties - Schedule of Revenues, Expenses and Amount Receivable with Entities Affiliated with Principal Owners (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureNetLossIncomePerShareAdditionalInformationDetail" id="DisclosureNetLossIncomePerShareAdditionalInformationDetail">
        <link:definition>996315 - Disclosure - Net (Loss) Income Per Share - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureNetLossIncomePerShareScheduleOfEarningsPerShareBasicAndDilutedDetail" id="DisclosureNetLossIncomePerShareScheduleOfEarningsPerShareBasicAndDilutedDetail">
        <link:definition>996325 - Disclosure - Net (Loss) Income Per Share - Schedule Of Earnings Per Share, Basic and Diluted (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SegmentInformationAndInformationAboutGeographicAreasAdditionalInformationDetail" id="SegmentInformationAndInformationAboutGeographicAreasAdditionalInformationDetail">
        <link:definition>996335 - Disclosure - Segment Information And Information About Geographic Areas - Additional Information (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SegmentInformationAndInformationAboutGeographicAreasScheduleOfRevenuesByGeographicAreaDetail" id="SegmentInformationAndInformationAboutGeographicAreasScheduleOfRevenuesByGeographicAreaDetail">
        <link:definition>996345 - Disclosure - Segment Information And Information About Geographic Areas - Schedule of Revenues by Geographic Area (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/SegmentInformationAndInformationAboutGeographicAreasScheduleOfSoftwareEquipmentAndPropertyNetByGeographicAreaDetail" id="SegmentInformationAndInformationAboutGeographicAreasScheduleOfSoftwareEquipmentAndPropertyNetByGeographicAreaDetail">
        <link:definition>996355 - Disclosure - Segment Information And Information About Geographic Areas - Schedule of Software, Equipment and Property, Net by Geographic Area (Detail)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://cccis.com/20230930/taxonomy/role/DisclosureGainOnSaleOfCostMethodInvestmentAdditionalInformationDetails" id="DisclosureGainOnSaleOfCostMethodInvestmentAdditionalInformationDetails">
        <link:definition>996365 - Disclosure - Gain on Sale of Cost Method Investment - Additional Information (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
    </xsd:appinfo>
  </xsd:annotation>
  <xsd:element id="cccs_PrepaidSoftwareAndEquipmentMaintenance" name="PrepaidSoftwareAndEquipmentMaintenance" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_NoncashLeaseExpense" name="NoncashLeaseExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_NumberOfTradingDaysUsedToDetermineTheSharePrice" name="NumberOfTradingDaysUsedToDetermineTheSharePrice" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_ClassesOfNonCurrentAssetAxis" name="ClassesOfNonCurrentAssetAxis" type="xbrli:stringItemType" substitutionGroup="xbrldt:dimensionItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_PhantomPlanMember" name="PhantomPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ShareBasedCompensationByShareBasedArrangementNonVestedOptionsOutstandingAggregateIntrinsicValue" name="ShareBasedCompensationByShareBasedArrangementNonVestedOptionsOutstandingAggregateIntrinsicValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_LeasesDisclosureOfLesseeTextBlock" name="LeasesDisclosureOfLesseeTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_LongTermDebtFloorRatePercentage" name="LongTermDebtFloorRatePercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="cccs_LiborMember" name="LiborMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_TimeBasedVestingMember" name="TimeBasedVestingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ClassOfWarrantOrRightsDateFromWhichWarrantsOrRightsExercisableExpired" name="ClassOfWarrantOrRightsDateFromWhichWarrantsOrRightsExercisableExpired" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_RevenueRemainingPerformanceObligationRevenueToBeRecognizedYearOne" name="RevenueRemainingPerformanceObligationRevenueToBeRecognizedYearOne" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_FairValueOfInterestRateCapAgreements" name="FairValueOfInterestRateCapAgreements" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_IncomeTaxDisclosureLineItems" name="IncomeTaxDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_AggregateNumberOfSharesReservedForSaleUnderPlanIncreasesOnBeginningOfPeriodPercentageOfTotalNumberOfSharesOutstandingOrLessorAmount" name="AggregateNumberOfSharesReservedForSaleUnderPlanIncreasesOnBeginningOfPeriodPercentageOfTotalNumberOfSharesOutstandingOrLessorAmount" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_PercentageOfSharesReservedForIssuanceUnderEmployeeIncentivePlan" name="PercentageOfSharesReservedForIssuanceUnderEmployeeIncentivePlan" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_TimeBasedVestingRequirementsMember" name="TimeBasedVestingRequirementsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_VestingCriteriaAxis" name="VestingCriteriaAxis" type="xbrli:stringItemType" substitutionGroup="xbrldt:dimensionItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_IncreaseDecreaseInDeferredCostsNonCurrent" name="IncreaseDecreaseInDeferredCostsNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_CapitalizedContractCostAdditionalAmountsDeferred" name="CapitalizedContractCostAdditionalAmountsDeferred" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_SharesAuthorizedTotal" name="SharesAuthorizedTotal" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_ShareBasedCompensationByShareBasedPaymentAwardNonVestedOptionsOutstandingWeightedAverageExercisePrice" name="ShareBasedCompensationByShareBasedPaymentAwardNonVestedOptionsOutstandingWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="cccs_PrepaidServiceFee" name="PrepaidServiceFee" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" name="FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_NumberOfConsecutiveTradingDaysUsedToDetermineTheSharePrice" name="NumberOfConsecutiveTradingDaysUsedToDetermineTheSharePrice" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_IntangibleAssetsAccumulatedAmortization" name="IntangibleAssetsAccumulatedAmortization" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_TwoThousandSeventeenStockPlanMember" name="TwoThousandSeventeenStockPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_TermBLoanMember" name="TermBLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_SafekeepincMember" name="SafekeepincMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_CorporateMinimumIncomeTax" name="CorporateMinimumIncomeTax" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="cccs_RedeemableNoncontrollingInterestTextBlock" name="RedeemableNoncontrollingInterestTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_SoftwareLicensesAndDatabaseMember" name="SoftwareLicensesAndDatabaseMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_AdjustmentsToEquityComponentDuringPeriodValueVestingSharesGrantedToStockholders" name="AdjustmentsToEquityComponentDuringPeriodValueVestingSharesGrantedToStockholders" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_LongTermPurchasingAgreementRelatingToLicensingDataUsedMember" name="LongTermPurchasingAgreementRelatingToLicensingDataUsedMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_SalesTaxProcessingServicesMember" name="SalesTaxProcessingServicesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_BasisOfAccountingPolicyTextBlock" name="BasisOfAccountingPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_LeaseCommencateMothYear" name="LeaseCommencateMothYear" type="xbrli:gYearMonthItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_LeasesTable" name="LeasesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_OtherServicesMember" name="OtherServicesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_AdditionalStockBasedCompensation" name="AdditionalStockBasedCompensation" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_SharePriceTriggeringEventAxis" name="SharePriceTriggeringEventAxis" type="xbrli:stringItemType" substitutionGroup="xbrldt:dimensionItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ContractWithCustomerAssetAndLiabilityTable" name="ContractWithCustomerAssetAndLiabilityTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_LongTermPurchaseCommitementAxis" name="LongTermPurchaseCommitementAxis" type="xbrli:stringItemType" substitutionGroup="xbrldt:dimensionItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_Rule10B51TradingPlanMember" name="Rule10B51TradingPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_WarrantLiablity" name="WarrantLiablity" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_IncreaseDecreaseInOperatingLeaseAssets" name="IncreaseDecreaseInOperatingLeaseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_PerformanceBasedVestingRequirementsMember" name="PerformanceBasedVestingRequirementsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_RevenueRemainingPerformanceObligationRevenueToBeRecognizedThereafter" name="RevenueRemainingPerformanceObligationRevenueToBeRecognizedThereafter" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_BusinessAcquisitionDisclosureTextBlock" name="BusinessAcquisitionDisclosureTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_PublicWarrantsMember" name="PublicWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_TwoThousandAndTwentyOneRevolvingCreditFacilityMember" name="TwoThousandAndTwentyOneRevolvingCreditFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_GoodwillAndIntangibleAssetsDisclosureLineItems" name="GoodwillAndIntangibleAssetsDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_PerformanceAndMarketBasedVestingConditionsMember" name="PerformanceAndMarketBasedVestingConditionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_DeferredRevenueRevenueRecognized" name="DeferredRevenueRevenueRecognized" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_EarningsPerSharesBasicAndDiluted" name="EarningsPerSharesBasicAndDiluted" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_PropertyPlantAndEquipmentNetMember" name="PropertyPlantAndEquipmentNetMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_PercentageOfAggregateCommitmentsOnBorrowings" name="PercentageOfAggregateCommitmentsOnBorrowings" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="cccs_StockIssuedDuringPeriodSharesStockOptionsExercisedNetOfTaxBenefitExpense" name="StockIssuedDuringPeriodSharesStockOptionsExercisedNetOfTaxBenefitExpense" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_EarningsPerSharesBasicAndDilutedOtherDisclosures" name="EarningsPerSharesBasicAndDilutedOtherDisclosures" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_LongTermPurchaseCommitementDomain" name="LongTermPurchaseCommitementDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_PerformanceBasedAwardsMember" name="PerformanceBasedAwardsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_EquipmentLeasesMember" name="EquipmentLeasesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_SponsorVestingSharesMember" name="SponsorVestingSharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_OwnershipInterestMember" name="OwnershipInterestMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ScheduleOfIntangibleAssetsTable" name="ScheduleOfIntangibleAssetsTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_DeferredTaxAssetsTaxDeferredExpenseTaxBenefitRecognizedImpairmentCharge" name="DeferredTaxAssetsTaxDeferredExpenseTaxBenefitRecognizedImpairmentCharge" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_EmployeeTaxObligationsMember" name="EmployeeTaxObligationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_TermLoansMember" name="TermLoansMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ScheduleOfRevenueByMajorCustomersByReportingSegmentsByServiceTableTextBlock" name="ScheduleOfRevenueByMajorCustomersByReportingSegmentsByServiceTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_CccCaymanMember" name="CccCaymanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_CompanyEarnoutSharesMember" name="CompanyEarnoutSharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_IncomeTaxDisclosureTable" name="IncomeTaxDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_OfficeSpaceAndDataCenterFacilitiesMember" name="OfficeSpaceAndDataCenterFacilitiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ImpairmentOfAcquiredTechnologies" name="ImpairmentOfAcquiredTechnologies" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_FiniteLivedIntangibleAssetsFutureAmortizationExpenseLineItems" name="FiniteLivedIntangibleAssetsFutureAmortizationExpenseLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ScheduleOfIntangibleAssetsLineItems" name="ScheduleOfIntangibleAssetsLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_SoftwareLicenseAgreementCurrent" name="SoftwareLicenseAgreementCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_ContractWithCustomerLiabilityTable" name="ContractWithCustomerLiabilityTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_RodneyChristoMember" name="RodneyChristoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_FiniteLivedIntangibleAssetsFutureAmortizationExpenseTable" name="FiniteLivedIntangibleAssetsFutureAmortizationExpenseTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_LongTermPurchaseCommitementMonthOfExpiry" name="LongTermPurchaseCommitementMonthOfExpiry" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_ClassesOfNonCurrentAssetDomain" name="ClassesOfNonCurrentAssetDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_LegalProceedingsAndContingenciesAbstract" name="LegalProceedingsAndContingenciesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_DeferredFinancingFeesRevolverNetNonCurrent" name="DeferredFinancingFeesRevolverNetNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_AccruedSalesTaxCurrent" name="AccruedSalesTaxCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_ContractWithCustomerAssetAndLiabilityLineItems" name="ContractWithCustomerAssetAndLiabilityLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_HumanResourceSupportServicesMember" name="HumanResourceSupportServicesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ShareBasedCompensationByShareBasedArrangementNonVestedOptionsOutstandingWeightedAverageRemainingContractualTerm" name="ShareBasedCompensationByShareBasedArrangementNonVestedOptionsOutstandingWeightedAverageRemainingContractualTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_AmortizationOfIntangibleAsset" name="AmortizationOfIntangibleAsset" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_SharePriceGreaterThanOrEqualToUsdFifteenPerShareMember" name="SharePriceGreaterThanOrEqualToUsdFifteenPerShareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesOfCommonStockProvidedRightToPurchase" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesOfCommonStockProvidedRightToPurchase" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_LeasesLineItems" name="LeasesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_IncreaseDecreaseInOperatingLeaseLiabilities" name="IncreaseDecreaseInOperatingLeaseLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_LongTermLicensingAgreementNetNonCurrent" name="LongTermLicensingAgreementNetNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_EmployeeHealthInsuranceBenefitsExpensesMember" name="EmployeeHealthInsuranceBenefitsExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_CorporateHeadquartersChicagoLllinoisMember" name="CorporateHeadquartersChicagoLllinoisMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_PrepaidSaasCosts" name="PrepaidSaasCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_DiscountRateBasedOnCostOfDebt" name="DiscountRateBasedOnCostOfDebt" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_PercentageOfWeightedAverageCostOfCapital" name="PercentageOfWeightedAverageCostOfCapital" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="cccs_GoodwillAndIntangibleAssetsDisclosureTable" name="GoodwillAndIntangibleAssetsDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_PercentageOfAnnualExcessCashFlowOnLineOfCredit" name="PercentageOfAnnualExcessCashFlowOnLineOfCredit" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_BusinessAcquisitionPotentialEarnOutAmount" name="BusinessAcquisitionPotentialEarnOutAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_EarningsPerSharesBasicAndDilutedAbstract" name="EarningsPerSharesBasicAndDilutedAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ScheduleOfGrossAmountAccumulatedImpairmentLossAndCarryingAmountOfGoodwillTableTextBlock" name="ScheduleOfGrossAmountAccumulatedImpairmentLossAndCarryingAmountOfGoodwillTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_LongTermLicensingAgreementNetCurrent" name="LongTermLicensingAgreementNetCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_IncreaseDecreaseInContingentConsiderationLiability" name="IncreaseDecreaseInContingentConsiderationLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_PrivateWarrantsMember" name="PrivateWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_FavorableLeaseTermsMember" name="FavorableLeaseTermsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_WarrantsTextBlock" name="WarrantsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_PercentageOfCompoundInterestPerAnnumOnThePreferredShareIssuePrice" name="PercentageOfCompoundInterestPerAnnumOnThePreferredShareIssuePrice" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_GainOnSaleOfCostMethodInvestmentDisclosureTextBlock" name="GainOnSaleOfCostMethodInvestmentDisclosureTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_ScheduleOfIntangibleAssetsTableTextBlock" name="ScheduleOfIntangibleAssetsTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_SoftwareLicenseAgreementNoncurrent" name="SoftwareLicenseAgreementNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_IncreaseDecreaseInDeferredCostsCurrent" name="IncreaseDecreaseInDeferredCostsCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_ClassOrWarrantIssuedPricePerShare" name="ClassOrWarrantIssuedPricePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_CostMethodInvestmentsCarryingValue" name="CostMethodInvestmentsCarryingValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_RedeemableNonControllingInterestPolicyTextBlock" name="RedeemableNonControllingInterestPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_CccFourHundredAndOneKRetirementSavingsAndInvestmentPlanMember" name="CccFourHundredAndOneKRetirementSavingsAndInvestmentPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_VestingCriteriaDomain" name="VestingCriteriaDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_TwoThousandAndTwentyOneCreditAgreementMember" name="TwoThousandAndTwentyOneCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_BoardOfDirectorFeesForServicesIncludingRelatedTravelAndOutOfPocketReimbursementsMember" name="BoardOfDirectorFeesForServicesIncludingRelatedTravelAndOutOfPocketReimbursementsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ContractWithCustomerLiabilityTableTextBlock" name="ContractWithCustomerLiabilityTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="cccs_MaryJoPriggeMember" name="MaryJoPriggeMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_AccruedRoyaltiesAndLicensesCurrent" name="AccruedRoyaltiesAndLicensesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_SoftwareSubscriptionsMember" name="SoftwareSubscriptionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_AcquiredTechnologiesMember" name="AcquiredTechnologiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ContractWithCustomerLiabilityLineItems" name="ContractWithCustomerLiabilityLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_UnamortizedFinancingCosts" name="UnamortizedFinancingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="cccs_CreditCardProcessingMember" name="CreditCardProcessingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_GainLossOnCostMethodInvestment" name="GainLossOnCostMethodInvestment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_CostMethodInvestmentsRecognizedGains" name="CostMethodInvestmentsRecognizedGains" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="cccs_CaymanEquityIncentivePlanMember" name="CaymanEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_CorporateStockRepurchaseExciseTaxRate" name="CorporateStockRepurchaseExciseTaxRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="cccs_LeverageRatio" name="LeverageRatio" type="xbrli:pureItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="cccs_Ccc2021EmployeeStockPurchasePlanMember" name="Ccc2021EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_SharePriceTriggeringEventDomain" name="SharePriceTriggeringEventDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="cccs_ContingentConsiderationRelatedToBusinessAcquisitionMember" name="ContingentConsiderationRelatedToBusinessAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
