Neb. Rev. Stat. §§ 46-118
The secretary of the board of directors must, as soon as the result is declared, enter in the records of such board a statement of such results, which statement must show (1) the whole number of votes cast in the district and in each division of the district; (2) the names of the persons voted for; (3) the office to fill which each person was voted for; (4) the number of votes given in each precinct for each of such persons; and (5) the number of votes given in the district for each of such persons. The board of directors must declare elected the person having the highest number of votes given for each office. The secretary must immediately make out and deliver to such person a certificate of election, signed by him and authenticated with the seal of the board. In case of a vacancy in the office of assessor or treasurer, the vacancy shall be filled by appointment by the board of directors. In case of a vacancy in the office of a member of the board of directors, the vacancy shall be filled by appointment by the two remaining members of the board and the district treasurer. An officer appointed as above provided shall hold his office until the next general election of the district and until his successor is elected and qualified.
Neb. Rev. Stat. §§ 46-118