Creates the Companion Animal Custody Equity Act. Provides that in a possession dispute involving a companion animal, a court may consider the well-being of the companion animal regardless of the marital status of the parties. "Companion animal" means a domesticated dog or cat that resides in a household. Authorizes the court to issue temporary possession or caregiving orders, including limited visitation, if necessary to reduce stress or disruption to the companion animal. Provides that for companion animals 10 years of age or older, courts may give additional consideration to factors including continuity of environment, emotional stability, stress minimization, and maintenance of established routines. Provides that a court may, if appropriate, order mediation between the parties to resolve issues related to companion animal possession.