I know of no reason that requires you to report an off post, non-government vehicle accident, with no arrest, or injuries.
If you were confined, arrested, detained, and/or it was a serious incident with serious injuries, death, transportation of individuals to a medical facility, drinking/drugs then I would say there is a definite requirement to report. The chain of command would use this information and send up a Serious Incident Report (SIR), if their reporting structure dictated such reporting.
If you seek medical attention from a military medical facility then you are required to tell them how you sustained the injury and they will sometimes coordinate with JAG to make a claim against the at fault party’s insurance.
The Army Safety Center has regulations and numerous tools and resources. I conducted a quick search and did not see anything here that required reporting under the conditions you stated.
I would encourage you to check out the site just to make sure for yourself. The last excuse you want to use is: “Hey 1SG I checked with some old CSM and he said I did not have to report the accident…” Hmm, what would follow would most likely not be a polite conversation 🙂