Conn. Gen. Stat. § 46b-115k: Initial child custody jurisdiction.

(a) Except as otherwise provided in section 46b-115n, a court of this state has jurisdiction to make an initial child custody determination if:

(1) This state is the home state of the child on the date of the commencement of the child custody proceeding;

(2) This state was the home state of the child within six months of the commencement of the child custody proceeding, the child is absent from the state, and a parent or a person acting as a parent continues to reside in this state;

(3) A court of another state does not have jurisdiction under subdivisions (1) or (2) of this subsection, the child and at least one parent or person acting as a parent have a significant connection with this state other than mere physical presence, and there is substantial evidence available in this state concerning the child's care, protection, training and personal relationships;

(4) A court of another state which is the home state of the child has declined to exercise jurisdiction on the ground that this state is the more appropriate forum under a provision substantially similar to section 46b-115q or section 46b-115r, the child and at least one parent or person acting as a parent have a significant connection with this state other than mere physical presence, and there is substantial evidence available in this state concerning the child's care, protection, training and personal relationships;

(5) All courts having jurisdiction under subdivisions (1) to (4), inclusive, of this subsection have declined jurisdiction on the ground that a court of this state is the more appropriate forum to determine custody under a provision substantially similar to section 46b-115q or section 46b-115r; or

(6) No court of any other state would have jurisdiction under subdivisions (1) to (5), inclusive, of this subsection.

(b) Subsection (a) of this section is the exclusive jurisdictional basis for making a child custody determination by a court of this state.

(c) Physical presence of, or personal jurisdiction over, a party or a child is not necessary or sufficient to make a child custody determination.