A: No.
Many times, the insurance company will try to convince you that you are required to give a "recorded statement." This is simply not true. In fact, it may be a terrible idea to give a statement to the insurance company.
First, insurance companies hire seasoned professionals who may try to trick you into saying something that will hurt your case.
Second, after a serious injury or wrongful death, you may not be in a position to give an accurate and complete statement.
Third, anything you say to the adjuster may be twisted and used against you after your injury.
Before giving a statement to the insurance company, seriously consider getting your own, independent legal advice.