Minn. Stat. § 134.10: BOARD VACANCIES; COMPENSATION.

The library board president shall report vacancies in the board to the council or the board of county commissioners. The council or board of county commissioners shall fill the vacancies by appointment for the unexpired term. Library board members shall receive no compensation for their services but may be reimbursed for actual and necessary traveling expenses incurred in the discharge of library board duties and activities or a per diem allowance according to section 375.47 in place of the expenses.