Do you have to report a minor car accident to police?

Of course you report accidents to the police; that's what they're for.

Another View: The answer to this will depend on the regulations of your individual state. Some do not take reports of minor, property-damage-only accidents - others only require reports of propertly damage accidents which exceed a certain dollar amount - etc. However, the one thing that is universal among all states, is the necessity to report an accident resulting in any claim of physical injury.