In all matters relating to the cooperative construction or improvement of any state highway, county road, or city or town street for which federal funds or aid is secured under any act of congress, the department shall act in the manner provided by state law relating to state highway construction from the motor vehicle fund, so far as the same may be consistent with the provisions of such act of congress and the rules and regulations made by the secretary of transportation or other authorized agent of the United States government pursuant to such act, to which the procedure shall be adapted by the department as may be necessary.