Yes, there is no question that you should wait for the police. Part of the job of the police is to make sure that legitimate, accurate information is obtained from each driver, including their name, address, insurance information, and information pertaining to the ownership of the vehicle. After they have performed their investigation, the officer will usually give you an “exchange sheet” which provides you with this information as to the other driver.
If you are going to rely on the trustworthiness of the other driver, who just ran into you, to provide you with accurate information, without the intervention of the police, then you are making a big mistake which could jeopardize your obtaining any recovery at all in your claim.
Also, if the damage to the vehicle is sufficient, it is also the job of police to perform a thorough investigation and draw up an accident report detailing the facts of the accident. That report is oftentimes crucial, and is always submitted to the insurance company with our demand package seeking money on your claim.