Do I have to give a recorded statement?
If the adjuster is working for the other driver's insurance company, you are not required to give a recorded statement. The insurance company wants to take your statement in order to begin building its case against you. Providing a recorded statement can do nothing to help your case, it can only hurt it. Therefore, if the adjuster from the other driver’s insurance company requests that you make a statement, politely refuse.
On the other hand, your relationship with your insurance company is established by your policy. It operates as a contract. You may be obligated by the rules of that policy to provide your company with a recorded statement if it requests one. Almost every policy states that to collect on a claim under that policy, you must cooperate with the insurance company and its investigation of the accident. It is a good idea to consult with an attorney prior to giving a recorded statement, even one to your own insurance company.