Yes, you should. Although we like to think people will do the right thing after causing a car crash, sometimes they don’t. So, you should begin protecting yourself immediately after the crash to help make sure you are treated fairly by the insurance company involved. The police will often have video and audio recordings (from the police car, body cameras, and body microphones) that can contain very valuable evidence that might be needed later in the claim or lawsuit.
Additionally, police are, in some circumstances, required by law to complete an investigative report, called a CR-3. This report will contain highly valuable information, such as identification of all the parties involved, insurance information, and an opinion of how the crash occurred. You might later need to rely on some of this information to help your case. Depending on the severity of the car crash, the police might complete a full accident investigation, complete with photographs and measurements, which can later serve as valuable evidence if a lawsuit is necessary.
Finally, the police will often interview witnesses to learn more about how a crash happened. Through this process (and the investigative process in general) documents are created that can later be obtained through an Open Records Request, and which contain information that might be useful in the event of a dispute about liability.