Any two or more hospital districts may merge into one district if a petition for merger is presented to the county board in the county which will include the greater portion of the proposed district by population and such merger is approved by a majority of the voters in the existing districts at an election as provided in section 23-3575. A petition for merger shall be sufficient if for each district affected by the proposed merger it has been either signed by a majority of the board of directors of each district or signed by the legal voters in each district equal to at least ten percent of the number of votes cast in such district for the Governor at the last general election. The petition shall be filed at least sixty days prior to any election.