Whenever the board of directors of any district deems it advisable to detach any portion of the district, which portion shall not have been apportioned for benefits, or having been apportioned, the amount having all been paid, the board of directors may submit at any annual election of the district the proposition of detaching such portion. If a majority of the votes cast on that question are in favor of the proposition to detach, the same shall be deemed carried, and the territory shall thereupon cease to be within the drainage district, and shall stand in the same plight as if never attached. The officers of the district shall certify the same to the county clerk, who shall make a record thereof.