Conn. Gen. Stat. § 52-102: Joinder of persons with interest adverse to plaintiff and of necessary persons.

Upon motion made by any party or nonparty to a civil action, the person named in the party's motion or the nonparty so moving, as the case may be, (1) may be made a party by the court if that person has or claims an interest in the controversy, or any part thereof, adverse to the plaintiff, or (2) shall be made a party by the court if that person is necessary for a complete determination or settlement of any question involved therein; provided no person who is immune from liability shall be made a defendant in the controversy.