Conn. Gen. Stat. § 52-284: Attachment against nonresident.

When the defendant is not a resident or inhabitant of this state and has estate within the same which has been attached, a copy of the process and complaint, with a return describing the estate attached, shall be left by the officer with the agent or attorney of the defendant in this state if known; and when land is attached, a like copy shall be left in the office of the town clerk of the town where the land lies. In addition, the court to which such action is returnable, or any judge, clerk or assistant clerk thereof shall make such order of notice to the defendant as is deemed reasonable to apprise him of the institution or pendency of such complaint and attachment. Such notice, having been given and proved, shall be deemed sufficient service of process in such action, and such attachment shall thereupon become effective against such estate and the defendant in such action.