I flew over Michigan once, so I don't know the laws there, or the ways things work... I can only talk about where I live, California. I mention this because there is no way I can give advice about Michigan, I can just tell you how it would work if it was in California.
Of course, your agent can explain this with knowledge of local laws. I would give him a call.
In California, you are supposed to report the accident to the DMV, if over a certain amount of damage happened (I don't know the $$$ limit, but 4 cars means it occured). Failure to do so can result in things like a suspended drivers license, fines, etc. If this happens, it shows up on your driving record, you're insurance company will find out about it anyway.
Also, an accident with a claim paid isn't always a rated incident. Lots of factors come into play. If you caused under a certain $$$ of damage, you would not be rated for the accident, even if the insurance company paid out.
You didn't mention how much damage was done, so it's hard to say what would happen, even if it happened here in California. I would highly suggest picking up the phone, talking to your personal agent, he'll guide you. I do this frequently, its what I get paid for.
Dan
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