S.D. Codified Laws § 31-14-35
It shall be lawful and the duty of the respective boards of county commissioners of the counties adjoining any highway or meandered stream on a county line in this state to divide that portion of such county line between such counties into two or more parts or districts, and to enter into an agreement and contract providing that each of such counties shall assume the liability and become responsible for the construction and maintenance of all necessary bridges upon such county line in the district allotted to such county. In case the stream forming the boundary between two counties shall be so large that one county alone is unable to build a bridge out of the ordinary amount of funds available, it shall be the duty of the two counties when a bridge is built over such stream to divide the expense equally between such two counties.
SDCL 31-14-35