Wis. Stat. § 17.28: When officers may hold office.

When no different provision is made in respect thereto, any officer who is elected or appointed to fill a vacancy shall qualify in the manner required by law of the officer in whose stead the officer is elected or appointed. An officer who is elected or appointed to fill a vacancy in an elective office shall enter upon the duties of his or her office immediately upon qualification and, if elected, upon certification of the election result, and shall hold office for the residue of the unexpired term unless removed or recalled in accordance with law except that an officer who is appointed to fill a vacancy in the office of sheriff, coroner, register of deeds or district attorney shall hold office until his or her successor is elected and qualified, unless removed or recalled in accordance with law. An officer who is appointed to fill a vacancy in an appointive office shall enter upon the duties of his or her office immediately upon qualification and shall hold office for the residue of the unexpired term, if any, and until his or her successor is appointed and qualifies unless removed in accordance with law.