If the county board determines that the allegations of said petition are not true, it shall deny the request. If it determines that the allegations of said petition are true, it shall, by resolution, declare that the county intends to assist in drainage under the provisions of sections 31-901 to 31-933. The determination and finding of the board shall be conclusive. If a county board has by resolution determined to assist and regulate drainage, it may at any time after one year has elapsed, by resolution, rescind such action and determine that the county assistance is not necessary. If the county board makes the determination to assist in drainage it shall have the authority provided for in sections 31-905 to 31-932.