The police and prosecutor will assume your story is bogus unless you have evidence to show that you really were in a car accident, such as the other driver's information, photos of the cars, photos of the damage, and the other driver's tag number. These are all things that the prosecutor will expect someone to have if they were in an accident.
Even if the other driver didn't have insurance, you should have. That means your own UM coverage would pay for the damage IF you called the police and made a report, but it doesn't sound like you did.
Without more evidence of a wreck, the prosecutor will assume you created this check yourself and cooked up the car wreck story as an explanation of where you got the check.
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