Vt. Stat. tit. 10 § 737
When the portion to be separated from a district and combined with another district does not comprise more than three towns, and the State Council has declared the move to be effective, that portion will come under the jurisdiction of the district to which it has been added. Where a supervisor resides in the portion of a district that has been added to another district, he or she shall resign and his or her successor shall be appointed by the remaining supervisors of the district where the vacancy occurs. When any district has had its boundaries so changed, the supervisors of the districts concerned shall apply to the Secretary of State for a new certificate of organization covering the area then within the district. If it is desirable to change the name of any district, the application shall so state. When the new certificate has been issued, the new district shall be duly organized and the old district which it replaces will cease to exist.
10 V.S.A. § 737