Conn. Gen. Stat. § 46b-115l: Jurisdiction.

(a) Except as otherwise provided in section 46b-115n, a court of this state which has made a child custody determination pursuant to sections 46b-115k to 46b-115m, inclusive, has exclusive, continuing jurisdiction over the determination until: (1) A court of this state or a court of another state determines that the child, the child's parents and any person acting as a parent do not presently reside in this state; or (2) a court of this state determines that (A) this state is not the home state of the child, (B) a parent or a person acting as a parent continues to reside in this state but the child no longer has a significant relationship with such parent or person, and (C) substantial evidence is no longer available in this state concerning the child's care, protection, training and personal relationships.

(b) A court of this state which has made a child custody determination but does not have exclusive, continuing jurisdiction under this section may modify that determination only if it has jurisdiction to make an initial determination under section 46b-115k.