When a petition signed by the state by the appropriate agency designated by the state administrative board which holds the record legal title to the entire area of the land in the territory to be annexed, which is adjacent to any city operating under a special charter, is filed with the governing body of the city and with the township board of the township in which the territory is situated, the annexation shall be accomplished by the affirmative majority vote of the qualified and registered electors of such city voting on the question, and the affirmative majority vote of the qualified and registered electors of such township voting on the question.

   The date of such election shall be determined by joint resolution of the governing body of the city and the township board, which date shall be at least 60 but not more than 90 days following the filing of the petitions unless a city or township election shall be held at least 45 but not more than 120 days from the date of the filing of the petition in which case such election shall be held on the same day as such city or township election. The governing body of the city and the township board shall forward a copy of the joint resolution to the county clerk of the county in which such city and township are located and the county clerk shall conduct such election in the same manner as county elections are conducted. All costs of ballots and other election supplies shall be borne by the city and township in proportion to the votes cast for governor in the last gubernatorial election.