Vt. Stat. Ann. tit. 17, § 2623

(1) In the event of a vacancy in any State, county, or legislative office, the Governor may request the political party or parties of the person whose death or resignation created the vacancy to submit one or more recommendations as to a successor. The proper committee to which a request for recommendation shall be directed shall be: for State officers, the State committee;

(2) for county officers, except justices of the peace and Probate judges, the county committee;

(3) for State Senator, the senatorial district committee;

(4) for State Representative, the representative district committee;

(5) for justice of the peace, the town committee;

(6) for Probate judge, the probate district committee.