(1) In any case in which the boundary line of an incorporated city extends in and along a public road, which road has not been paved or macadamized, then the county board of any county in which such road lies is hereby authorized and empowered to maintain and keep in repair and proper condition for travel the full width of such road, including the portion which lies within the corporate limits as well as the portion which lies outside of the corporate limits, and to pay the cost and expense of such maintenance, repair, and upkeep, so long as the road remains unpaved.
(2) A county may enter into an agreement under the Interlocal Cooperation Act with a city or village located in such county to appropriate and use county road funds for the improvement, maintenance, or repair of a road or street that is:
(a) Located within the corporate limits of the city or village if the street is classified as other arterial, collector, or local under subdivisions (4) through (6) of section 39-2104 and such street acts as a direct link or extension of an other arterial as described in subdivision (5) of section 39-2103;
(b) Located on the boundary between the corporate limits of the city or village and the county; or
(c) A city or village road or street directly impacted by county operations or through traffic.