If they find that you had an accident but didn’t file a claim with them, it would probably be recorded at the insurance company as an “IBNR”–that is, Incurred But Not Reported. I don’t know what this would do to your insurance premiums; the insurer may just raise them anyway, since having been convicted of causing an accident, you now represent a higher risk. Assuming you are convicted, SoulSearching; I’ll give you the benefit of the doubt for now.
I do agree with amarone–that you read your insurance policy closely and do what it says. Depending on what it says; yes, you may have to report it to the insurer and your rates may go up. But you may also avoid having to give a “yes” answer to the dreaded “have you ever been refused” question if it is posed in the future.
You will probably want to report this to your insurance company right away. Insurers take an extremely dim view of clients who do not do so. There are many cases where an insurance company is blind sided by a claimant from an unreported accident. This usually occurs long after the fact and makes the validity of outstanding claims difficult to verify. You may be dropped by your insurer if you do not report this accident to them immediately.
In the future NEVER admit to anything at the scene of an accident. Provide your name, address and driver’s license number. Answer the officer’s questions to the best of your ability but defer any requests for information to your attorney if you feel the answer may incriminate you. I am not a lawyer nor do I play one on television. This closing bit of advice came from a sitting Alameda county judge my sister knew. It has proven quite sound over the years.