In this video, Sevenish Law answers the question: How soon should I report the accident to my insurance company?
You should call as soon as you reasonably can. Many insurance contracts set a deadline for reporting accidents. If you miss that deadline, you may not be able to make any claim at all. Waiting too long might also make the insurance company believe you are exaggerating your injuries, which allows it to deny your claim for failing to make timely notice and/or other reasons. So to protect your interests, whether you believe you are at fault or not it is wise to report the claim so it can be assigned a claim number. However, even if it is your own insurance company you should not give a recorded statement without guidance from an experienced injury lawyer.