Neb. Rev. Stat. § 16-503

On the passage or adoption of every resolution or order to enter into a contract, or accepting of work done under contract, by the mayor or city council of a city of the first class, the yeas and nays shall be called and entered upon the record. To pass or adopt any bylaw or ordinance or any such resolution or order, a concurrence of a majority of all elected members of the city council shall be required. The mayor may vote on any such matter if (1) the mayor's vote is required due to the city council members being equally divided or (2) a majority vote of all the elected members of the city council cannot be reached due to absence, vacancy, or abstention of one or more city council members. For purposes of such vote, the mayor is deemed to be a member of the city council. The requirements of a roll call or viva voce vote shall be satisfied by a city which utilizes an electronic voting device which allows the yeas and nays of each city council member to be readily seen by the public.