Kan. Stat. § 68-412
After the secretary of transportation shall deem it advisable for the proper completion of the state highway system to designate any city street as a connecting link in the state highway system, the secretary may assist said city on the state highway system in the construction, improvement and reconstruction of said streets as hereinafter set out. The type of such construction, improvement and reconstruction shall be determined by agreement between the city and the secretary of transportation, and the construction shall be under the supervision of the secretary.
The cost of construction, improvement and the reconstruction of such streets and highways, shall be apportioned between the department of transportation and such city, to be determined by an agreement between the city and the secretary of transportation. The portion of such cost to be paid by the secretary shall be paid from that portion of the state highway fund provided for construction of state highways and the cost of the remainder of such street highways shall be paid by the city from a fund raised in the manner provided by law for the payment for grading, curbing, guttering and paving streets in such city: Provided, That in no event shall the secretary of transportation be liable for construction, improvement or reconstruction as herein set out unless the secretary shall have designated such streets as connecting links in the state highway systems: And provided further, That the secretary of transportation shall decide the time when such construction, improvement or reconstruction shall be commenced.
Where any such improvement shall receive federal aid, the secretary of transportation may, in the secretary's discretion, use any such federal funds that may be available for such purpose, to assist the city in the payment of such a part of the city's portion of the cost of such improvement as the secretary may deem proper or advisable.
K.S.A. 68-412