Conn. Gen. Stat. § 2-16: Members as attorneys before the General Assembly.

No member of the General Assembly shall appear as an attorney before it, or before any committee thereof, or of either house, unless in his own cause, or that of the town which he represents or of some public corporation therein, or where there is so near a relation between such member and either of the parties as between parent and child, brothers, sisters, brother and sister, uncle and nephew or niece, aunt and nephew or niece, by nature or marriage, or landlord and tenant.