A. The governing body of a district shall consist of five supervisors, three of whom are to be elected and two appointed by the commissioner. Except as to the first supervisors, whose election and terms are prescribed in section 37-1035, the term of each elected supervisor shall be six years, beginning on June 1 following his election. As prescribed in section 37-1036, the terms of the two supervisors appointed by the commissioner shall be until May 31 of the next even-numbered year, or until their successors are otherwise appointed.

B. An election shall be held on the first Saturday in May of each even-numbered year, at which one supervisor of the district shall be elected. Any person desiring to be a candidate shall file with the commissioner a nomination petition in such form as the commissioner prescribes, at least ten days prior to the election, containing the signatures of not less than twenty-five qualified electors of the district. No person shall be eligible to be a candidate for supervisor unless he is a qualified elector of the district. The names of candidates shall appear on the ballot in alphabetical order by surnames, with a square after each name and an instruction to mark an X in the square after the name of the voter’s choice. The governing body of a district may provide a mail ballot to a qualified district elector for which the district governing body has a first class mailing address. Qualified electors of a district who wish to vote by mail ballot shall file a first class mailing address with the district governing body at least thirty days prior to the date of the election. Qualified district electors who receive ballots in proper form from the district governing body may cast their votes by mail. Mail ballots, to be counted, shall be received at the place designated, and within the time prescribed by the district supervisors and clearly specified in the notice of election. Only qualified electors of the district shall have the right to vote. The district governing body shall provide at least one polling place in the district for qualified voters who wish to vote in person. If two or more candidates receive the same number of votes, the successful candidate shall be determined by lot.