Conn. Gen. Stat. § 52-137: Amendment changing the relief sought.

If, on the trial upon an issue of fact or of law of an action in which equitable relief is demanded, it appears that the plaintiff is not entitled to equitable relief, but may be entitled to legal relief, the court may allow the complaint to be amended so as to present a proper case for legal relief. In like manner a complaint demanding legal relief may be amended to entitle the plaintiff to equitable relief.