Kan. Stat. § 68-716
The petition as provided for in K.S.A. 68-701 may be for the improvement of a road or roads situated in more than one county or upon the county line between two counties. A certified copy of the petition shall be transmitted by the clerk of the county in which it is filed to the board of county commissioners of the adjoining county and after the approval and granting thereof by the county commissioners of each of said counties the several county boards may act in conjunction in carrying on said improvements under the provisions of this act. The assent of the majority of the members of each board shall be required in all proceedings.
A contract for the construction of a road in more than one county may be let, bids may be advertised for, proposals filed and the contract let at the county seat of either of the counties as the two boards shall direct. The cost as between two counties and the townships and benefit districts therein, shall be apportioned according to the area of the benefit districts in each county: Provided, That when a major portion of the road petitioned for lies within one county and the remaining portion lies on the county line between two counties, and part of the benefit district lies in each county, the cost shall be apportioned as follows: After deducting all federal aid, state aid and other donations, the remainder of the cost of that portion of the road lying entirely within one county shall be apportioned: fifty percent (50%) to the county; twenty-five percent (25%) to the taxable property within the township or townships in which the benefit district is situated, divided according to the area of the benefit district in each township; and twenty-five percent (25%) among the several tracts of land within the benefit district; the cost of the road on the county line after deducting all federal aid and state aid and other donations shall be apportioned as follows: twenty-five percent (25%) to each county; twelve and one-half percent (121/2%) to each county to be assessed against the taxable property of the township adjacent to said road; and in case two or more townships in one county lie adjacent to the county line road, the apportionment between the townships shall be on the ratio of the mileage of the road to be improved adjacent to each township; and twelve and one-half percent (121/2%) of the cost of the county line road shall be apportioned to each county to be assessed against the land in the benefit district.
After the ascertainment of the division of cost between the two counties and the total apportionment to the townships and benefit district in each and the application of state and federal aid and donations, the county boards shall act separately in carrying out the provisions of this act and shall make the assessments against each tract of land in the benefit district of each county in the manner provided in this act.
K.S.A. 68-716