If the other driver leaves the scene of the accident, you need to call the police immediately. Leaving the scene of an accident is a criminal offense.
Calling the police as soon as possible will accomplish two important things. First, it will increase the likelihood that they are able to locate the other party, which will make your car accident case much simpler because you will have an insurance company with whom you can file your claim.
Second, calling the police will ensure that your accident has proper evidence. There may be witnesses who can attest to the fact that the other driver was involved.
A police report alone is crucial evidence, as the officers can attest to the fact that an accident did, in fact, take place at the date time and location that you are claiming it did. You may still be able to pursue your claim if the driver is never located, but it will be extremely difficult to do so without evidence of your accident.
If the other driver leaves, call the police.