Conn. Gen. Stat. § 52-337: Service on bank or trust company as garnishee.

Whenever a bank, savings bank, trust company or industrial bank is named as garnishee, process shall be served by leaving a copy thereof with any officer or teller at the garnishee's principal office during its regular hours of business; provided, whenever a branch of any such bank or trust company which is located in a different town from the one in which the principal office of such bank or trust company is located is named as garnishee, process shall be served by leaving a copy thereof with any officer or teller at such branch during its regular hours of business.