Insurance companies typically request that a claim be made promptly and within a reasonable amount of time. Some states might have a law or statute that regulates this and thus dictates that the claim must be made within a certain time period, such as a year. You can contact your state's insurance regulator or department of motor vehicles to find out what the time limit might be set at in your specific state.
This time period would generally be the same whether there was a police report made or not. If you are the one filing a claim, you might have to explain why there was not a police report filed and why you delayed reporting the incident to the insurance carrier. The insurance company will then investigate the claim to decide if it is valid or not and if they will cover the loss.