A city or village may establish and maintain a museum pursuant to sections 51-501 to 51-513 when approved by at least fifty-one percent of the votes cast at the election by the electors of the city or village voting on the proposition. Notwithstanding the provisions of any home rule charter to the contrary, any city or village which established a museum prior to April 10, 1957, or any city or village contracting for the use of a museum already established shall not be required to hold an election to contract for or to establish and maintain such a museum for any term of years deemed necessary or advisable by such city or village. When the electors of a city or village approve the establishment and the maintenance of a museum pursuant to sections 51-501 to 51-513, the city council or village board shall establish and maintain a museum pursuant to such sections. Such city or village shall appoint a museum board of not less than five but not more than nine members to be chosen from the citizens of the city or village at large. Except as further provided in this section, neither the mayor nor any member of the city council or village board shall be a member of the museum board. The members of the museum board first appointed shall hold office, the first for a term of one year, the second for a term of two years, the third for a term of three years, the fourth for a term of four years, the fifth for a term of five years, the sixth for a term of one year, the seventh for a term of two years, the eighth for a term of three years, and the ninth for a term of four years from the first day of July following their appointment. As their terms expire, one member shall be chosen annually thereafter for a term of five years. In cases of vacancies by resignation, removal, or otherwise, the city council or village board shall fill such vacancy for the unexpired term. Cities having home rule charters may fix by ordinance the number of members of such museum board. No member shall receive any pay or compensation for any services rendered. However, the city council of any city or the board of trustees of any village which is contracting for the use of a museum already established shall be the museum board and may establish the city council or board of trustees as the museum board without regard to the requirements for terms and numbers of members on the board set forth in this section.