Parking a non-running car on the street.
 

My car got into an accident and is not drivable right now. How ever, it still have insurance. Can I park it on the street?

The Tow truck driver said I can't leave it on the street even though it has insurance. By-law will come and impound the car if I do. I can't really find a topic like this anywhere. Thanks.

You have to put it in the garage or privatE property if it doesn't have insurance.
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your city will have by-laws stating how long you can park it for consecutive periods. Some cities only allow you to park it for 72 hours at a time in specific zones. If it has insurance, then yes, you can park it, but it depends on how long you want to leave it there for.

This is for Vancouver

The Parking Enforcement Branch enforces Section 13(1)(b) and (c) of the Motor Vehicle Act which prohibits derelict and/or unlicensed vehicles from being left on Vancouver streets or laneways. Vehicles left on City property for an extended period of time with an accumulation of dust, dirt or leaves on and around the vehicle, damage or in obvious disrepair and/or expired insurance are indicators of an abandoned vehicle. Vehicles parked on city streets must have valid registration and current insurance.

City of Vancouver By-Law 3519 authorizes the immediate impounding of vehicles, trailers or other chattels unlawfully occupying city streets or highways.

Park Smart: Don't Abandon Your Vehicle

Yes you are perfectly fine to park it on the street.
When my girlfriends car got rear ended. the rear bumper was mangled and the trunk wouldnt close. It would bang up and down and close and open and ICBC told us it was drivable.

Winsons604 posts summarized: If it looks abandoned, even if its insured, it might get towed. Damaged doesn't mean abandoned unless you have homeless people living in it, spider webs, and leaves.