Neb. Rev. Stat. §§ 32-1121
If any candidate failed to be nominated or elected by more than the margin provided in section 32-1119, the losing candidate may submit a certified written request for a recount at such candidate's expense. The request shall be filed with the filing officer with whom the candidate filed for election not later than the fifth day after the county canvassing board or the board of state canvassers concludes. The recount shall be conducted as provided in section 32-1119. Prior to conducting the recount, the cost of the recount shall be determined by the election commissioner or county clerk and the requesting candidate shall be so notified. The candidate requesting the recount shall pay the estimated cost of the recount before the recount is scheduled to be conducted. If the recount involves more than one county, the election commissioner or county clerk shall certify the cost to the Secretary of State. The Secretary of State shall then notify the candidate of the determined cost, and the cost shall be paid before any recount is scheduled to be conducted. The candidate shall pay the cost on demand to the county treasurer of each county involved, and such sums shall be placed in the county general fund to help defray the cost of the recount. If the actual expense is less than the determined cost, the candidate may file a claim with the county board for overpayment of the recount. If the recount determines the candidate to be the winner, all costs which he or she paid shall be refunded. Refunds shall be made from the county general fund.
Neb. Rev. Stat. §§ 32-1121