Conn. Gen. Stat. § 46b-321: Continuing, exclusive jurisdiction to modify spousal support order.

(a) A tribunal of this state issuing a spousal support order consistent with the law of this state has continuing, exclusive jurisdiction to modify the spousal support order throughout the existence of the support obligation.

(b) A tribunal of this state may not modify a spousal support order issued by a tribunal of another state or a foreign country having continuing, exclusive jurisdiction over that order under the law of that state or foreign country.

(c) A tribunal of this state that has continuing, exclusive jurisdiction over a spousal support order may serve as (1) an initiating tribunal to request a tribunal of another state to enforce the spousal support order issued in this state; or (2) a responding tribunal to enforce or modify its own spousal support order.