Jurisdictional responsibility for the various functional classifications of public highways and streets shall be as follows:

(1) The state shall have the responsibility for the design, construction, reconstruction, maintenance, and operation of all roads classified under the category of rural highways as interstate, expressway, and major arterial, and the municipal extensions thereof, except that the state shall not be responsible for that portion of a municipal extension which exceeds the design of the rural highway leading into the municipality. When the design of a rural highway differs at the different points where it leads into the municipality, the state's responsibility for the municipal extension thereof shall be limited to the lesser of the two designs. The state shall be responsible for the entire interstate system under either the rural or municipal category and for connecting links between the interstate and the nearest existing state highway system in rural areas, except that if such a connecting link has not been improved and a sufficient study by the Department of Transportation results in the determination that a link to an alternate state highway would provide better service for the area involved, the department shall have the option of providing the alternate route, subject to satisfactory local participation in the additional cost of the alternate route;

(2) The various counties shall have the responsibility for the design, construction, reconstruction, maintenance, and operation of all roads classified as other arterial, collector, local, minimum maintenance, and remote residential under the rural highway category;

(3) The various incorporated municipalities shall have the responsibility for the design, construction, reconstruction, maintenance, and operation of all streets classified as expressway which are of a purely local nature, that portion of municipal extensions of rural expressways and major arterials which exceeds the design of the rural portions of such systems, and responsibility for those streets classified as other arterial, collector, and local within their corporate limits; and

(4) Jurisdictional responsibility for all scenic-recreation roads and highways shall remain with the governmental subdivision which had jurisdictional responsibility for such road or highway prior to its change in classification to scenic-recreation made pursuant to this section and sections 39-2103, 39-2109, and 39-2113.