What are the requirements on reporting an accident to insurance company if it is not your fault?

Most companies do not require you to report the accident to your own insurance company, but if you later find out the person did not have valid insurance or the other insurance company refuses to pay and then you later have to file a claim on your policy, it will slow down the claim process. Plus, each state has a statute on the time limit you have to file a claim and want it to be covered.