Conn. Gen. Stat. § 46b-527
During the period after the date of execution of a surrogacy agreement until the occurrence of the earlier of the date of termination of a surrogacy agreement pursuant to the agreement terms, or ninety days after the date of birth of a child conceived by assisted reproduction under the surrogacy agreement, a court of this state conducting a proceeding under sections 46b-450 to 46b-553, inclusive, has exclusive, continuing jurisdiction over all matters arising out of the agreement. The provisions of this section do not give the court jurisdiction over a child custody proceeding or a child support proceeding if jurisdiction is not otherwise authorized by the law of this state other than the provisions of sections 46b-450 to 46b-553, inclusive,.
Conn. Gen. Stat. § 46b-527