Neb. Rev. Stat. §§ 51-201.07
If the city council, village board, or township board and library board, if one exists, both adopt a resolution indicating that such city, village, or township library no longer desires to be a part of the county library system and notify the county board by filing the resolutions with the county clerk, the county board shall submit the question to the voters of the city, village, or township at the next statewide general election. If a majority of the voters voting on the issue vote to withdraw from the county library, then beginning on January 1 following the election, the city, village, or township shall cease to be entitled to the benefits of such county library and the property situated in such city, village, or township library shall not be liable for taxes levied for county library purposes. The city council, village board, or township board and the county board shall enter into a dissolution agreement to provide for the disposition of assets, indebtedness, and employees. If the parties cannot agree within one year after the election, either party may bring an action in the district court and the district court shall determine the disposition of assets, indebtedness, and employees.
Neb. Rev. Stat. §§ 51-201.07