Conn. Gen. Stat. § 52-55: When completion of service by another officer allowable.

(a) If an officer to whom any process is directed dies or is removed from office, or becomes physically incapacitated, or because of other good and sufficient reason is unable to complete service of the process, after he has commenced to serve it but before completing service, any other proper officer may complete service.

(b) If the term of office of any officer to whom any process is directed and who has commenced to serve it expires before the completion of service, he may nevertheless proceed to complete service in the same manner and with the same effect as if he still remained in office.