Kan. Stat. § 68-1122
If a county bridge or culvert be necessary on any public highway that is on or near to a county line or divides one county from another in this state, the boards of both counties may unite in the construction, repairing and maintenance of such structure; and the expense shall be defrayed by both counties in proportion to their assessed valuation on the last assessment rolls, unless the boards of county commissioners of the counties shall agree upon another distribution of such expense.
Either of the said counties may give notice to the other of the meeting of said boards for the purpose mentioned in this section, and in all such cases the same proceedings, so far as applicable, shall be as provided for in this act: And provided, That under similar conditions two townships, whether they be in the same or different counties, may unite and proceed in the same manner as required in this act for the construction, repair and maintenance of township bridges and culverts: And provided further, That if a bridge or culvert be necessary on a public highway that is on or near to a state line the county or township, as the case may be, may unite with the county or township of such adjoining state in the construction, repair and maintenance of such structure as herein provided: Provided further, That should there be a demand for a county bridge or culvert upon or near a county line, and the county commissioners of the respective counties cannot agree upon the construction or repair of such a bridge or culvert, then the matter shall be referred to the secretary of transportation, the decision and direction of which shall be binding upon the boards of county commissioners of both counties; and in case of a township bridge or culvert the same shall be referred to the board of county commissioners, who shall proceed in the manner described above, and their decision shall be final and binding on the boards of township commissioners of both townships.
K.S.A. 68-1122