In real life the cops would have caught him very quickly
Now, inevitably, the next few lines may reveal some part(s) of the movie which nitpickers may construe as spoilers, so if you don't want to know what they are, look away now.
Policemen have very suspicious minds and they would not simply accept Chris's story that he had reversed over the litterlout who had allegedly walked behind the 'van without looking. He didn't just reverse, he drove over the guy at full tilt! A normal driver would have (a) not reversed that quickly and (b) would have slammed on the brakes at the first bump, not carry on driving — unless he intended to drag the victim under the wheels. Besides, I doubt that the perp would be allowed to carry on his way, blood-spattered wheels and all. The cops would have wanted to impound the 'van until the matter had been cleared up.
Meanwhile the cops would have asked around if anyone knew where the litterlout had been during the previous few days. He had people with him, so they would have told the detectives that they'd been at a tram museum. These relatives would remember the altercation between the perp and the litterlout over the sweet wrapper, and the cops would then immediately start to question whether Chris had an ulterior motive for killing him to get revenge.