S.D. Codified Laws § 62-4-40
If compensation is awarded under this title, the employer having paid the compensation, or having become liable therefor may collect in the employer's own name or that of the injured employee, or the employer's personal representative, if deceased, from any other person against whom legal liability for damage exists, the amount of the liability. The employer shall hold for the benefit of the injured employee or the employee's personal representative, if deceased, the amount of damages collected in excess of the amount of compensation paid the employee or the employee's representative, less the proportionate necessary and reasonable expense of collecting the same, which expenses may include an attorney's fee not in excess of thirty-five percent of damages so collected, and shall be subject finally to the approval of the department.
SDCL 62-4-40