Kan. Stat. § 68-436
When the secretary of transportation has agreed to schedule an improvement project to begin construction within one year, and that local participation in supplying funds is desirable, the board of county commissioners of any county may participate with the state, by providing funds for the state's share of any highway improvement in the county. Such funds shall be provided either from the proceeds of bonds issued under K.S.A. 10-1201 or K.S.A. 68-434, and amendments thereto. The secretary of transportation may contract with any county regarding the repayment of all or any part of any funds furnished by such county and may provide for the repayment thereof from the state highway fund. If such funds are derived from the proceeds of bonds issued pursuant to K.S.A. 10-1201, and amendments thereto, any repayment thereof shall be deposited in the county general fund and distributed between the county and the cities in the manner provided by K.S.A. 12-192, and amendments thereto. If such funds are derived from bonds issued pursuant to K.S.A. 68-434, any repayment thereof shall be deposited in the county road and bridge fund.
No contract authorized by this section shall be entered into after July 1, 1986.
K.S.A. 68-436