Giving a recorded statement to the other driver’s insurance company is generally not recommended. You are not obligated to give a recorded statement, and once you are on the phone, it is hard to be in control of the conversation. You may not be aware what information can be used against you later.
If the the other party was clearly at fault for causing the accident, the insurance company really does not need your recorded statement. The insurance company will have access to the accident report and can talk to the at-fault driver. That should be all they need to conclude an investigation. On the other hand, if there is some dispute about who is at fault for causing the accident, you should consult with an attorney before giving a statement. Either way, giving a recorded statement to the at-fault driver’s insurance company is generally not recommended. A request for one may be politely declined.
If you are making an uninsured or underinsured motorist claim against your own insurance company, then you probably cannot decline to give a statement. You probably have a duty under your insurance policy to cooperate with your insurance company’s investigation. Failure to cooperate with your insurance company might invalidate your claim. If you are uncomfortable giving a statement to your insurance company, than seeking advice of a lawyer before giving one is certainly reasonable.