A petition to submit separate tax limitations to the electors of the county also may be initiated by a resolution adopted by a majority of the members of a county tax allocation board. The petition shall be in substantially the same form and processed in the same manner as provided in this act for initiatory petitions signed by registered electors of the county. The question shall be submitted to a vote of the registered and qualified electors of the county subject to the same conditions and in the same manner as an initiatory petition signed by registered electors. The ballot shall be in substantially the same form, and subsequent to the vote the same proceedings shall be had, as provided in this act.