Conn. Gen. Stat. § 51-39: Disqualification by relationship or interest. Judge or family support magistrate may act with consent of parties.

(a) Except as provided in this section, a judge or family support magistrate is disqualified to act if a relationship between the judge or family support magistrate and a party in any proceeding in court before him is as near as the degree of kinship between father and son, brothers, or uncle and nephew, by nature or marriage, or as near as between landlord and tenant, or if any judge or family support magistrate may be liable to contribute to the damages, costs or expenses of any proceeding before him, or if he may receive a direct pecuniary benefit by the determination of any proceeding before him.

(b) A judge or family support magistrate shall not be disqualified to act in any proceeding by reason of his being a member of any ecclesiastical corporation, unless it is a party to the action, nor in any proceeding in which any town, city or borough is interested or is a party, by reason of his being an inhabitant thereof or liable to taxation therein or by reason of his being related to any taxpayer or inhabitant thereof.

(c) When any judge or family support magistrate is disqualified to act in any proceeding before him, he may act if the parties thereto consent in open court.