An amendment to enlarge the boundaries of a metropolitan district may be initiated by a petition signed by 5% of the registered voters residing in the area sought to be added to the district. The petition shall be filed with the clerk and the legislative body of the city, village, or township in which the proposed added area is located, which legislative body may pass a resolution requesting the metropolitan district legislative body to hold an election on an amendment to its charter to include the proposed added area within its boundaries. Upon filing the resolution with the district’s clerk, if the legislative body of the district approves the resolution by a 3/5 vote, an election shall be held in the proposed added area and the district to vote on the proposed charter amendment as provided in section 9. If the district and the proposed added area each approves the proposed amendment by a majority vote of those voting in the election, the metropolitan district’s charter shall be amended accordingly.