Within 60 days of the effective date of this act, petitions may be filed with the secretary of state, signed by a number of registered electors from a county within the authority equal to at least 5% of the total vote cast for all candidates for governor at the last preceding general election at which a governor was elected within the petitioning county, requesting that the county’s participation in the authority be submitted for approval by a majority of the electors of the county voting at the next general election in the manner provided by law.