Conn. Gen. Stat. § 46b-115z: Simultaneous proceedings.

If a proceeding for enforcement under this chapter is commenced in a court of this state and the court determines that a proceeding to modify the determination is pending in a court of another state having jurisdiction to modify the determination under a provision substantially similar to section 46b-115k, 46b-115l or 46b-115m, the enforcing court shall immediately communicate with the modifying court. The court of this state shall proceed with the action for enforcement of the child custody determination unless the court, after consultation with the modifying court, stays or dismisses the proceeding.