Whenever, upon the trial to fix and assess the benefits and damages resulting from the construction of any diking or drainage system under the laws of this state, the jury shall find by its verdict that any public or county road will be benefited from the construction of such improvement, the clerk of the court in which such trial is had shall, upon the entry of the judgment upon such verdict, certify to the board of county commissioners of the county in which such road is situated the amount of benefits to such road so found and adjudged. The said county commissioners shall, upon the receipt of such certified statement, allow the same as for other road work and shall order the amount thereof to be paid out of the road and bridge fund of the road district in which the road so benefited is situated, and shall direct the auditor of said county to issue a warrant for the amount of such benefits against the road and bridge fund of such road district in favor of the county treasurer of said county. The said county treasurer shall, upon the payment of said warrant, place the proceeds therefrom to the credit of the drainage or diking district from which such benefits resulted.