Conn. Gen. Stat. § 46b-316: Continuing jurisdiction to enforce child support order.

(a) A tribunal of this state that has issued a child support order consistent with the law of this state may serve as an initiating tribunal to request a tribunal of another state to enforce (1) the order if the order is the controlling order and has not been modified by a tribunal of another state that assumed jurisdiction pursuant to the Uniform Interstate Family Support Act; or (2) a money judgment for arrears of support and interest on the order accrued before a determination that an order of a tribunal of another state is the controlling order.

(b) A tribunal of this state having continuing jurisdiction over a support order may act as a responding tribunal to enforce the order.