Whenever the board of county commissioners of any county having a population of less than four thousand inhabitants is petitioned so to do by twenty percent of the qualified electors of such county, as determined by the vote cast for the office of governor at the last preceding general election, such board shall submit to the qualified electors of the county the question of disorganization of the county. The question shall be submitted at the next statewide election occurring more than ninety days after the filing of such petition.