Conn. Gen. Stat. § 7-103

Unless otherwise provided by law, any elected or appointed town, city or borough officer, except the town, city or borough clerk, desiring to resign from his office shall submit his resignation in writing to the town, city or borough clerk, as the case may be; and any such clerk desiring to resign from his office shall submit his resignation in writing to the board of selectmen, the chief executive officer of the city or the chief executive officer of the borough, as the case may be. Any such resignation shall become effective upon the date specified therein or, if no date is so specified, upon the date of its submission.