Upon the filing of a petition for dissolution with the county clerk by persons owning not less than twenty-five percent of the territory of the district, the board shall set a time and place for hearing as set forth in sections 39-1641 and 39-1642. At the hearing the board may pass a resolution dissolving the district. The board shall perform all acts necessary to wind up the affairs of the district. All funds remaining after discharge of the district’s indebtedness shall be deposited in the general fund of the county.