Conn. Gen. Stat. § 33-663: Service of process on corporation.

(a) A corporation's registered agent is the corporation's agent for service of process, notice or demand required or permitted by law to be served on the corporation. Service may be effected by any proper officer or other person lawfully empowered to make service by leaving a true and attested copy of the process, notice or demand with such agent or, in the case of an agent who is a natural person, by leaving it at such agent's usual place of abode in this state.

(b) If a corporation has no registered agent, or the agent cannot with reasonable diligence be served, the corporation may be served by any proper officer or other person lawfully empowered to make service by sending a true and attested copy of the process, notice or demand by registered or certified mail, return receipt requested, addressed to the secretary of the corporation at its principal office. Service is effective under this subsection at the earliest of: (1) The date the corporation receives the mail; (2) the date shown on the return receipt, if signed on behalf of the corporation; or (3) five days after its deposit in the United States mail, as evidenced by the postmark, if mailed postage prepaid and correctly addressed.

(c) This section does not prescribe the only means, or necessarily the required means, of serving a corporation.