No. These statements are designed so that you have a high chance of incriminating yourself. They do not need this statement to process your claim, and you aren’t required to tell them anything about the incident.
When they ask for a recorded statement, politely decline, ask for their contact information, and tell them that you’ll have your attorney get in touch with them soon.
If you already gave the insurance company a statement, don’t worry. Your case isn’t lost. Many other people in your position have made this same mistake before. Contact a lawyer as soon as you can to put your case on the right path forward.