A petition seeking the withdrawal of real property from such district, signed by persons owning not less than twenty-five percent of the territory proposed to be withdrawn may be filed with the county clerk. 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 permitting the withdrawal of the proposed territory. Any area withdrawn from the district shall be subject to assessment and be otherwise chargeable for the payment and discharge of all the obligations outstanding at the time of filing the petition for withdrawal. An area withdrawn from a district shall not be subject to assessment or otherwise chargeable for any obligations of any nature or kind incurred after the withdrawal of the area from the district.