Conn. Gen. Stat. § 1-101oo

(b) Where personal jurisdiction is based solely upon this section, an appearance does not confer personal jurisdiction with respect to causes of action not arising from an act enumerated in this section.

(c) Any nonresident person or the agent of such person over whom the Office of State Ethics may exercise personal jurisdiction, as provided in subsection (a) of this section, who does not otherwise have a registered agent in this state for service of process, shall be deemed to have appointed the Secretary of the State as the person's or agent's attorney and to have agreed that any process in any complaint, investigation or other matter conducted pursuant to section 1-82 or 1-82a , concerning an alleged violation of section 1-101nn and brought against the nonresident person, or such person's agent, may be served upon the Secretary of the State and shall have the same validity as if served upon such nonresident person or agent personally. The process shall be served upon the Secretary of the State by the officer to whom the same is directed by leaving with or at the office of the Secretary of the State, at least twelve days before any required appearance day of such process, a true and attested copy of such process, and by sending to the nonresident person or agent so served, at the person's or agent's last-known address, by registered or certified mail, postage prepaid, return receipt requested, a like and attested copy with an endorsement thereon of the service upon the Secretary of the State. The Secretary of the State shall keep a record of each such process and the day and hour of service.