Conn. Gen. Stat. § 52-61: Service upon nonresident fiduciaries.

Process in civil actions against a nonresident executor, administrator, conservator, guardian or trustee, in his representative capacity, or in his individual capacity in any action founded upon or arising from his acts or omissions as such executor, administrator, conservator, guardian or trustee, may be served by leaving a true and attested copy thereof with the judge of probate or probate court that appointed the nonresident executor, administrator, conservator, guardian or trustee, and such judge or court shall forthwith give notice thereof to such executor, administrator, conservator, guardian or trustee.