Wis. Stat. § 17.24

Except as provided in s. 9.10, a vacancy in any elective village office may be filled by appointment by a majority of the members of the village board for the residue of the unexpired term or until a special election is held, as ordered by the village board, or an office may remain vacant until an election is held. A vacancy in an appointive office shall be filled in the same manner as the original appointment.