Conn. Gen. Stat. § 52-384

If, after demand made as provided in section 52-383 , a writ of scire facias is issued against such garnishee, and he still remains without this state, service of such writ shall be made in such manner as the judge or clerk of the court rendering judgment in the original suit, by a written order thereon by him subscribed, directs, and by leaving with his agent or attorney, if any has been appointed by him in the manner provided in section 52-383 , a true and attested copy of the writ; and process so issued and served shall be as effectual against such garnishee as if served upon him personally.