Conn. Gen. Stat. § 52-193: Offer of compromise by defendant.

In any action on contract, or seeking the recovery of money damages, whether or not other relief is sought, the defendant may, not later than thirty days before trial, file with the clerk of the court a written offer of compromise signed by the defendant or the defendant's attorney, directed to the plaintiff or the plaintiff's attorney, offering to settle the claim underlying the action for a sum certain.