(1)(a) Except as otherwise provided in subsection (2) or (3) of this section or section 32-568, vacancies in city and village elected offices shall be filled by the mayor and council or board of trustees for the balance of the unexpired term. Notice of a vacancy, except a vacancy resulting from the death of the incumbent, shall be in writing and presented to the council or board of trustees at a regular or special meeting and shall appear as a part of the minutes of such meeting. The council or board of trustees shall at once give public notice of the vacancy by causing to be published in a newspaper of general circulation within the city or village or by posting in three public places in the city or village the office vacated and the length of the unexpired term.
(b) The mayor or chairperson of the board shall call a special meeting of the council or board of trustees or place the issue of filling such vacancy on the agenda at the next regular meeting at which time the mayor or chairperson shall submit the name of a qualified registered voter to fill the vacancy for the balance of the unexpired term. The regular or special meeting shall occur upon the death of the incumbent or within four weeks after the meeting at which such notice of vacancy has been presented. The council or board of trustees shall vote upon such nominee, and if a majority votes in favor of such nominee, the vacancy shall be declared filled. If the nominee fails to receive a majority of the votes, the nomination shall be rejected and the mayor or chairperson shall at the next regular or special meeting submit the name of another qualified registered voter to fill the vacancy. If the subsequent nominee fails to receive a majority of the votes, the mayor or chairperson shall continue at such meeting to submit the names of qualified registered voters in nomination and the council or board of trustees shall continue to vote upon such nominations at such meeting until the vacancy is filled. The mayor shall cast his or her vote for or against the nominee in the case of a tie vote of the council. All council members and trustees present shall cast a ballot for or against the nominee. Any member of the city council or board of trustees who has been appointed to fill a vacancy on the council or board shall have the same rights, including voting, as if such person were elected.
(2) The mayor and council or chairperson and board of trustees may, in lieu of filling a vacancy in a city or village elected office as provided in subsection (1) of this section or subsection (3) of section 32-568, call a special city election to fill such vacancy.
(3) If vacancies exist in the offices of one-half or more of the members of a city council or village board, the Secretary of State shall conduct a special city election to fill such vacancies.