No you don’t need a police report to make an insurance claim after a car accident. You should call the police if someone is hurt, if there is significant damage to the cars or if you think the driver of the other car is guilty of a criminal offence (e.g. drunk driving). If for some reason you don’t call the police you should at least report the crash to the police accident centre.
You can report the car accident to your insurance company even though you haven’t called the police or reported the car crash. Your insurance adjuster may ask you to report the accident to the police accident centre.
In any case you must always get the name and address of the driver, license plate number of the car, and full insurance details of the driver.
For a full run down of what to do in a motor vehicle accident please see: “I was in a motor vehicle accident. What should I do?”.