The answer to this question depends on which adjuster calls you and the purpose of the call.
The other driver's insurance adjuster
If the other driver's insurance company calls you, you have no duty to speak with him regarding your claim. However, with that being said, there are two types of claims in a routine car accident. The first claim relates to your property damage, which pertains to getting your car fixed or totaled. Many personal injury lawyers do not handle property damage claims. When it comes to property damage, some attorneys allow the insurance adjuster to speak with the client about the vehicle only. In these situations, the adjuster may ask you about the facts of the accident generally, but there is no reason for a recorded statement.
Regarding an injury claim, it is not advisable to give a recorded statement to the adverse driver's insurance company. You may want to talk to the adjuster informally about the facts of the accident, but a recorded statement is out of the question for my clients.
Your Insurance Company
If you've been injured in the accident, you will need to open a PIP (personal injury protection) claim, which will pay for your initial medical expenses. Your insurance adjuster has an absolute right to take a record statement under the terms of your insurance policy. Insurance policies have two clauses that apply in this situation: (1) the duty to cooperate; and (2) a specific clause that requires an insured who is making a claim under the policy to give a statement, if requested.
Sometimes folks get confused when multiple parties in an accident have the same insurance company. When this situation arises, it is important to ask who the adjuster represents when they call. If they represent the other driver, then the rules that pertain to “adverse drivers” apply. If the adjuster is the adjuster signed to “your claim”, you are required to speak to her.