Kan. Stat. § 68-506g
Whenever any county major collector road or county minor collector road is located partly within and partly without a city or connects any such road or highway with a city, by and with the consent of the governing body, the board of county commissioners is hereby given power and authority and required to designate such public road or highway as a part of the county road or highway system. Such road or highway shall be improved and maintained as other parts of the county road system, except that the governing body of such city may aid in the construction, maintenance and improvement of such road or highway as it would were the road or highway wholly within the corporate limits of the city and may improve any such city boundary line road or street in the manner provided by K.S.A. 12-693, and amendments thereto. When a road or highway is being, or has been improved by the county where state or federal aid has been extended in the improvement of such road or highway, and such road or highway terminates at the city limits, and where a road or highway has been or shall be constructed with federal aid, which such road or highway terminates at a state line, and the state line is the corporate limits of a city within this state, the secretary of transportation is hereby authorized and empowered to extend federal aid, and the board of county commissioners, on the application of the governing body of the city, shall declare such city through which a street or streets form a connection between such roads or highways, a benefit district, and shall extend state aid on that part of the road or highway lying within the city limits in the same way and in the same manner as they extend aid in the improvement of the road or highway outside of the city limits. The secretary of transportation is hereby authorized and empowered to cooperate and deal with the governing body of the city, board of county commissioners, or other interested parties that provide funds to take care of the local part of the costs of the improvement of the road or highway lying within the city limits, and such improvement shall be under the supervision and direction of the secretary as provided for in the improvement of other roads and highways of like nature in the county.
K.S.A. 68-506g