It all depends. If it’s the wrongdoers or the at-fault party’s insurance company that is contacting you, asking you to give a statement after the crash, the answer is no. You have no privity with that insurance company, that being the insurance company for the party that caused the accident.

However, if it is your insurance company that you have privity with, you do have a responsibility that’ll be in your insurance contract to work with them after the accident for them to evaluate the claim and that can include providing them with a statement, but with respect to the entity that caused the accident, the person that’s at fault for the accident, you need not provide their insurance company with a statement, you should speak with a lawyer before you give a statement to any insurance company for the at-fault party.