Conn. Gen. Stat. § 52-406: Submission of agreed case.

Parties to a question in difference which might be the subject of a civil action between them may, without action, agree upon a case containing the facts upon which the controversy depends and submit the case to any court in the judicial district in which either of them resides, in which an action might have been brought to determine the controversy. If it appears by affidavit of the parties, or their respective attorneys, that the controversy is real and the proceeding is submitted in good faith to determine the rights of the parties, the court shall, on payment of the court and clerk fees, as on trial, hear and determine the case and render judgment thereon. The judgment shall be entered as in other cases, but without including costs, and may be enforced in the same manner as if it had been rendered in an action.