Yes. In fact, you need to distinguish between your insurance company the company that you purchased insurance from. You have an obligation under the insurance contract and the law in most states to cooperate with your insurance company with the investigation of the accident. You also have an obligation under the insurance contract and law to notify your insurance company of the accident or the wreck.
The next question would be should you speak to the insurance company of the other vehicle or vehicles involved in the wreck. The answer to that is almost always no.
If something has escalated to the point where you need to notify an insurance company of a wreck or an injury, you should at least consult by phone with an experienced injury attorney.
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