You are under no legal obligation to give the insurance company a recorded statement following a car accident—and it’s almost never in your best interests to do so.
While it may seem innocent or even procedural, the only reason for an insurance company to request a recorded statement is to potentially use your own words against you later. An insurance adjuster’s job is always to save the company money, and they are only looking for information that can be used to limit their liability or downplay the extent of your injuries.
Providing a recorded statement is not inherently bad, but it likely means there’s some sort of dispute between both drivers’ stories. Many insurance adjusters will use trick questions and leading statements to get the answers they’re looking for, and will often seek a recorded statement well before you even have a full understanding of your injuries.
Always speak with your attorney first, but if you do give a recorded statement, be honest, forthcoming, and stick to the facts.