In most cases, tow-truck drivers hook up the car and tow it without having to open the car or access it at all. If the car had any noticible odor from the outside, the tow-truck driver had a bad cold and didn't smell it.
Once at the impound yard there's no reason to open it either. The VIN number is visible through the windshield, driver's side, in the lower corner. They likely send the license plate number to the state Dept. of Motor Vehicles to obtain the registered owner of the vehicle.
I think that when Casey left that car at Amscot it was already beginning to smell. Once at the impound yard, there was no reason to open the car. It sat unopened for more than two weeks before George picked it up. In that time, sitting in the hot sun, that odor grew stronger and permeated the entire car. George said that he drove the car home with the windows down and had nausea. Cindy found Casey's slacks in the back seat and they "smelled like the car", so she washed them.