If any such permit is refused by the mayor and council or other governing body of any municipal corporation for the operation of any theater or athletic event, game, or contest, as the case may be, within the limits of such municipal corporation or such refusal is made by the board of county commissioners or other governing official or governing body of the county as to theaters or as to such events, games, or contests, as the case may be, within the county but outside of any municipal corporation, then upon the presentation of a petition to the mayor and council or the governing body of any municipal corporation or to the board of county commissioners or other governing official or governing body of the county, if the theaters or the places for holding such athletic events, games, or contests lie outside the limit of any municipal corporation, bearing the names of at least 25 percent of the registered voters of the municipal corporation or county, as the case may be, requesting that the permits be issued, then it shall be the duty of the governing bodies of the municipal corporations or counties, as the case may be, to issue the permits.