Neb. Rev. Stat. §§ 31-306
Within thirty days after the district court shall have declared any drainage district organized, the clerk of the court shall, upon fifteen days' notice, call a meeting of the owners of the real estate situated in the district, at the day and hour specified, in some public place in the county in which the district was organized, for the purpose of electing a board of five supervisors to be composed of owners of real estate in the district and a majority of whom shall be residents of the county or counties in which such district is situated. At such election every acre of land shall represent one share and each owner shall be entitled to one vote for every acre of land owned by him in such district. The five persons receiving the highest number of votes shall be declared elected as supervisors, and they shall immediately, by lot, determine their terms of office, which shall be respectively, one, two, three, four and five years, and until their successors are elected and qualified; Provided, however, at any time thereafter not more often than once in twelve months, upon the petition of the owners of at least twenty percent of the land acreage within the drainage district, an election shall be called for the selection of a new board, and upon the filing of such petitions with the secretary of the board, notice of such election shall be given by the secretary in the same manner and for the same time as is provided for at the original election under the notice given by the clerk of the district court. Special elections shall in all respects be governed by the provisions applicable to the regular election herein provided for.
Neb. Rev. Stat. §§ 31-306