1.    Except as otherwise provided in this section, every vehicle stopped or parked upon a two-way roadway must be so stopped or parked with the right-hand wheels of such vehicle parallel to and within twelve inches [30.48 centimeters] of the right-hand curb or as close as practicable to the right edge of the right-hand shoulder.

2.    Except where otherwise provided by local ordinance, every vehicle stopped or parked upon a one-way roadway must be so stopped or parked parallel to the curb or edge of the roadway, in the direction of authorized traffic movement, with its right-hand wheels within twelve inches [30.48 centimeters] of the right-hand curb or as close as practicable to the right edge of the right-hand shoulder, or with its left-hand wheels within twelve inches [30.48 centimeters] of the left-hand curb or as close as practicable to the left edge of the left-hand shoulder.

3.    Local authorities may by ordinance permit angle parking on any roadway, except that angle parking is not permitted on any federal-aid or state highway without first obtaining the written authorization of the director.

4.    The department with respect to highways under its jurisdiction may place official traffic-control devices prohibiting or restricting the stopping, standing, or parking of vehicles on any highway where in its opinion such stopping, standing, or parking is dangerous to those using the highway or where the stopping, standing, or parking of vehicles would unduly interfere with the free movement of traffic thereon. No person may stop, stand, or park any vehicle in violation of the restrictions indicated by such devices.

5.    The department, with respect to streets, roadways, and parking areas of any state charitable or penal institution and on the state capitol grounds, may authorize the purchase and placement by the supervisory agency of official traffic-control devices prohibiting or restricting the stopping, standing, or parking of vehicles. The placement of signs pursuant to this section must be done when, in the department’s opinion, the stopping, standing, or parking is dangerous or would unduly interfere with the free movement of traffic, especially the free flow of traffic required for proper fire protection. No person may stop, stand, or park any vehicle in violation of the restriction indicated by any official traffic-control device. Any registered owner must be presumed to have been the operator of a vehicle that is parked in violation of any official traffic-control device prohibiting or restricting the stopping, standing, or parking of vehicles on any highway, state charitable or penal institution property, or on the state capitol grounds. This presumption may be rebutted by a showing of clear and convincing evidence to the contrary. However, no traffic citation may be issued for a violation of this subsection occurring on the state capitol grounds during a legislative session, except that a written warning must be placed on any vehicle for such a violation.