Conn. Gen. Stat. § 46b-312: Duration of personal jurisdiction.

Personal jurisdiction acquired by a tribunal of this state in a proceeding under sections 46b-301 to 46b-425, inclusive, or other law of this state relating to a support order continues as long as a tribunal of this state has continuing, exclusive jurisdiction to modify its order or continuing jurisdiction to enforce its order as provided by sections 46b-315, 46b-316 and 46b-321.