Conn. Gen. Stat. § 52-409: Stay of proceedings in court.

If any action for legal or equitable relief or other proceeding is brought by any party to a written agreement to arbitrate, the court in which the action or proceeding is pending, upon being satisfied that any issue involved in the action or proceeding is referable to arbitration under the agreement, shall, on motion of any party to the arbitration agreement, stay the action or proceeding until an arbitration has been had in compliance with the agreement, provided the person making application for the stay shall be ready and willing to proceed with the arbitration.