Conn. Gen. Stat. § 46b-115x

A court of this state shall recognize and enforce, but not modify except in accordance with section 46b-115m , a child custody determination of a court of another state if (1) the court of the other state exercised jurisdiction under a provision substantially similar to section 46b-115k , 46b-115 l or 46b-115m , the determination was made under factual circumstances meeting the jurisdictional standards of this chapter and the determination has not been modified in accordance with this chapter, or (2) the child custody determination was registered in this state pursuant to section 46b-115w . A child custody determination which satisfies the criteria in subdivision (1) or (2) of this section shall have the same effect and shall be enforced in the same manner as a child custody determination rendered by the Superior Court.