S.D. Codified Laws § 31-14-39
If a petition is filed with the board of county commissioners of either county affected thereby, praying for the building, altering, or repairing of any bridge described in § 31-14-38, and the petition is found to comply with the law relating to petitions for bridges, it shall be the duty of the board of county commissioners of such county immediately to cause a copy of such petition to be filed with the county auditor of the other county to be affected thereby, and at the same time to give the commissioners of such county notice of the time and place when and where the commissioners will meet to consider such petition. At such meeting of the county commissioners of the two counties jointly affected thereby, they shall view the site of such bridge, and if such petition is granted, then by agreement between such commissioners either county may build, alter, or repair such bridge and one-half the cost shall be borne by each of such counties.
SDCL 31-14-39