The directors of state institutions, and the Game and Parks Commission and natural resources districts for areas under their control, shall have the powers of local authorities provided for in the Nebraska Rules of the Road with regard to roadways running through, within, or along the grounds of the institution or area which are not part of the state highway system and not within the limits of any incorporated city or village. The governing body of an incorporated city or village may delegate to the director of a state institution, or to the Game and Parks Commission or a natural resources district for an area under its control, responsibility for regulating traffic and placing and maintaining traffic control devices on roadways not part of the state highway system running through or within the limits of such institution or area and within the incorporated city or village when such city or village does not exercise its right to regulate traffic on such roadway.