Whenever a petition signed by three-fourths of the landowners in any district organized under the provisions of sections 46-1001 to 46-1020 is presented to the county board and it shall appear from such petition that such district owns no property of any kind, exclusive of records, maps, plans and files; that all of its debts and obligations have been fully paid; that the board of directors has not held a meeting for more than one year prior to the date of signing such petition; that the district is not functioning, and will probably continue to be inoperative, the county board shall, after such finding, issue a certificate stating the allegations in such petition as true and declaring such district dissolved, and shall make full minutes of such hearing in its records and deliver such certificate to the secretary of such district. The secretary of such district shall, within thirty days thereafter, deliver all records, maps, plans and files to the county clerk, and thereupon such district shall be dissolved.