A county may join an existing multicounty consolidated government by resolution of the board of supervisors or upon petition of eligible electors of the county equal in number to at least twenty-five percent of the persons who voted at the last general election for the office of governor or president of the United States, whichever is fewer. Within fifteen days after receiving a valid petition, the board of the petitioning county shall adopt a resolution in favor of participation and shall immediately forward the resolution to the legislative body of the multicounty consolidated government. If a majority of the multicounty consolidated board of supervisors approves the resolution, the question of joining the multicounty consolidated government shall be submitted to the electorate of the petitioning county within sixty days after approval of the resolution.