After a car accident, you're under no obligation to give anyone a statement. However, you are under obligation to cooperate with your own insurance company. What we'd advise you to do is immediately contact an attorney, such as our firm, and we can help guide you through these particular issues. Any statement you give to another insurance company, they may use against you. They may misrepresent or misstate something that occurred, and that could be detrimental to your case later. The answer to the question is no.