Minn. Stat. § 375.04: TIE DETERMINED BY LOT.

If two or more persons have an equal and the highest number of votes for the office of county commissioner in a district, the auditor shall give written notice to them to attend at the auditor's office at a time specified. The auditor shall then and there, in their presence, publicly decide by lot which shall be declared elected. The person selected shall be the commissioner from the district.