S.D. Codified Laws § 31-14-27
If a township board of supervisors or county highway superintendent requests the board of county commissioners to construct or replace in its entirety any bridge or the placing or replacing of any culvert with an opening of sixteen square feet or more including material upon the secondary roads within the township, the board of county commissioners may cause the work to be done and the township shall reimburse the county up to and including five hundred dollars. If the cost is in excess of five hundred dollars, the county and township may enter into an agreement as to how the cost in excess of five hundred dollars will be split between the county and the township. After the placing or replacing of any culvert as provided in this section, the culvert shall be maintained and kept clean at the expense of the township. The construction or replacing of any bridge or the placing or replacing of any culvert with an opening of less than sixteen square feet upon a secondary road within a township shall be at the total expense of the township. The bridge or culvert shall be maintained and kept clean at the expense of the township.
SDCL 31-14-27