What do you do if you accidentally bumped a car in a parking lot then left a note with iPhone number but the person did not call?

The statute of limitations varies from state to state, but if the owner of the vehicle has not called after a sufficiently long period of time that a person under normal circumstances would have been presumed to call, then you are absolved from any wrong doing.... if you hit the car in a public parking area, it is a no-fault accident and each respective insurance policy would have to pay for repairs unless proven (or admitted) fault is established. and there is no one to exchange information with, then there must have been no driver in that car, and therefore your vehicle must have been the only one in motion and that would almost certainly mean you were at fault.