Conn. Gen. Stat. § 52-80: Nonsuits and withdrawals; costs.

If the plaintiff, in any action returned to court and entered in the docket, does not, on or before the opening of the court on the second day thereof, appear by himself or attorney to prosecute such action, he shall be nonsuited, in which case the defendant, if he appears, shall recover costs from the plaintiff. The plaintiff may withdraw any action so returned to and entered in the docket of any court, before the commencement of a hearing on the merits thereof. After the commencement of a hearing on an issue of fact in any such action, the plaintiff may withdraw such action, or any other party thereto may withdraw any cross complaint or counterclaim filed therein by him, only by leave of court for cause shown.