Minn. Stat. § 169.35: PARKING.

Subdivision 1. Parallel to curb.

Except where angle parking is permitted by local ordinance, each vehicle stopped or parked upon a two-way roadway where there is an adjacent curb shall be so stopped or parked with the right-hand wheels of the vehicle parallel with and within 12 inches of the right-hand curb, provided, that such exception shall only apply to a state trunk highway after approval by the commissioner.

Subd. 2. Where no curb.

Upon streets and highways not having a curb each vehicle stopped or parked shall be stopped or parked parallel with and to the right of the paved or improved or main-traveled part of the street or highway.

Subd. 3. One-way roadway.

Local authorities with respect to streets and highways under their jurisdiction and with the consent of the commissioner with respect to state trunk highways may by ordinance permit parking of vehicles with the left hand wheels adjacent to and within 12 inches of the left hand curb of a one-way roadway.