Conn. Gen. Stat. § 52-135: Amendment of pleadings after default or demurrer overruled; costs.

The plaintiff, in any cause of action for unliquidated damages in which a default has been entered, or in which a judgment has been rendered upon a demurrer to the complaint overruled, may, at any time before final judgment, amend his complaint on the payment of costs, at the discretion of the court; but, after any such amendment, the defendant shall have a reasonable time to file an answer to the same.