Neb. Rev. Stat. §§ 51-203
When the county board of any county or the electors of any township vote to establish and maintain a public library, the county board or the township board shall establish a library board. The library board shall have at least five members. No member of the county board or township board shall be a member of the library board. The county board or township board shall determine by resolution the number of members, whether the members are elected or appointed, and the length of the terms of the members. The terms of members serving on the effective date of a change in the number of members shall not be shortened, and the county board or township board shall provide for the appointment or election of their successors. Such county or township board shall have the power to fill for the unexpired term any vacancy which may occur in the county or township library board. No member shall receive any pay or compensation for any services rendered as a member of such board.
If the county board or township board provides for appointment of the members to the library board, such library board members shall be appointed by a majority vote of the members of the county board or township board. If the county board or township board provides for the election of library board members, the election shall be held in conjunction with the statewide primary election as provided in the Election Act and the county board or township board shall give public notice of such election after the adoption of such resolution naming the offices to be filled, the length of terms, and the filing deadline for the placing of names of candidates on the ballot.
Neb. Rev. Stat. §§ 51-203