Minn. Stat. § 471.46: VACANCIES; PERSONS INELIGIBLE TO APPOINTMENT.

No county, city, town, or school district officer shall be appointed to fill a vacancy in any elective office if the officer has the power, either alone or as a member of a board, to make the appointment; and the ineligibility shall not be affected by resignation before such appointment is made. This section shall not prevent the appointment of a member of a city council to the office of mayor or clerk, but in that case the member shall not vote in the appointment.