Minn. Stat. § 1.51

Each American flag and Minnesota flag flown on the grounds of the Capitol Area, as described in section 15B.02 , must be flown at half-staff following the death of a public safety officer, as defined in section 299A.41, subdivision 4 , killed in the line of duty in Minnesota, or the death of Minnesota military personnel killed in the line of duty. The flags must be flown at half-staff for a period of time determined by the governor.