My response:
Assuming your accident DID NOT involve alcohol or other intoxicants; e.g., there are no criminal charges pending against you, then give the statement. If there are criminal charges pending against you, DO NOT give anyone a statement unless counsel is present at all times.
On the dreary side of this accident, you've bought a rental car, and you've bought all the damages and pain and suffering incurred by the other party as a result of your negligence.
Whether or not there are criminal charges against you - - or just merely civil negligence involved, I would strongly recommend that you invest in a good defense attorney for your criminal and/or civil liability exposure.
Good luck.
IAAL
------------------
By reading the “Response” to your question or comment, you agree that: The opinions expressed herein by "I AM ALWAYS LIABLE" are designed to provide educational information only and are not intended to, nor do they, offer legal advice. Opinions expressed to you in this site are not intended to, nor does it, create an attorney-client relationship, nor does it constitute legal advice to any person reviewing such information. No electronic communication with "I AM ALWAYS LIABLE," on its own, will generate an attorney-client relationship, nor will it be considered an attorney-client privileged communication. You further agree that you will obtain your own attorney's advice and counsel for your questions responded to herein by "I AM ALWAYS LIABLE."