Insurance company claims guidelines can differ but normally no, you do not have to have a police report for an accident in order to file a claim. This is generally true for an accident that took place on private property or elsewhere.
While it is usually helpful to those involved in the accident, as well as the insurance companies, to have a police report taken most insurance providers are aware that police cannot always make it to the scene of an accident and thus just request the accident participants to exchange information. Also in some certain areas and jurisdictions law enforcement refuses to respond to accidents that take place on private property.
If possible it is usually best to get a police or accident report to turn into the insurance carrier with your claim. Our article How To Deal With Your Insurance Company Regarding Claims may be of help to you if you are placing a claim with your insurance provider.