(a) The provisions of this article prohibiting the standing or parking of a vehicle shall apply at all times or at those times herein specified or as indicated on official signs except when it is necessary to stop a vehicle to avoid conflict with other traffic or in compliance with the directions of a police officer or official traffic-control device.
(b) The provisions of this article imposing a time limit on parking shall not relieve any person from the duty to observe other and more restrictive provisions prohibiting or limiting the stopping, standing or parking of vehicles in specified places or at specified times.
(c) When signs are erected giving notice thereof, no person shall park a vehicle at any time upon any of the streets so posted. When signs are erected or painted on a curb or sidewalk in each block giving notice thereof no person shall park a vehicle for longer than three consecutive days in any space where unrestricted parking is permitted, and in event any vehicle is parked for more than three consecutive days the Police Department is hereby given permission and authority, at the discretion of the Chief of Police, or the acting Chief, to order the removal of such vehicle to a parking lot or private parking stall or garage without notice to the owner, and the owner thereof shall thereupon be responsible for any tow bill and storage bill which shall accumulate upon the vehicle by reason of such towing and storage.