When the secretary of transportation has agreed to schedule an improvement project to begin construction within one year and has agreed that local participation in supplying funds is desirable, the governing body of any city may participate with the state by providing funds for the state’s share of any highway improvement in the city. Such funds may be provided from the proceeds of bonds issued under Kan. Stat. Ann. § 68-437. The secretary of transportation may contract with any city regarding the repayment of all or any part of any funds furnished by such city and may provide for the repayment thereof from the state highway fund. If such funds are derived from bonds issued pursuant to Kan. Stat. Ann. § 68-437, any repayment thereof shall be deposited in the city general fund.