YES! Witnesses often leave the scene of a collision once they find out that no one was hurt. As such it will often come down to your word against the other driver as to the cause of the collision. Each driver blames the other in which case the Court won’t know who to believe if a law suit is necessary.
Calling the police insures that an independent, credible witness comes to the scene, takes down statements, collects evidence, and maps the scene. This information will become invaluable should a suit be necessary, and your car accident attorney will be able to make use of this information. Most people don’t know that skid marks can disappear in hours along with evidence such as critical pieces of the car. Getting an accurate diagram prevents this loss.
Recently, as a car accident attorney, I had a case in which a collision occurred after the plaintiff pulled out onto a highway and was rear-ended. The defendant told the police that she was unable to slow down in time. Only months later did the defendant change her story to “the other car pulled out suddenly and I was unable to stop.” After the plaintiff sued for damages to his car, the defendant sued for damages to her car. Were it not for the presence of the police, her story might have prevailed and she would have recovered money for an accident she caused.
Bottom line: Call the police to report any collision. It will pay dividends down the road and protect you from a suit.