Neb. Rev. Stat. §§ 23-3539
A petition seeking the annexation of additional land to such district, signed by the legal voters in the area proposed for annexation equal in number to ten percent of the number of votes cast in the area for Governor at the last general election, may be filed with the board of directors. The board shall submit the question of annexation of such area to the legal voters of the district and of the area proposed for annexation, which question shall be submitted at the next annual hospital district election. If a majority of those voting on the question in the district and a majority of those voting on the question in the area proposed for annexation vote in favor of annexation, the board of directors shall declare such area annexed and certify the altered boundaries of the district to the county board of the county in which the annexed area is located and of the county in which the greater portion of the district is located.
Neb. Rev. Stat. §§ 23-3539