To be convicted of damaging their car they will need evidence you did it. That will mean credible witness evidence, not just their say so, but generally that would require either an independent witness or video footage. Likely if there is no such credible evidence the police will not charge you, despite their allegations.
Conversely, if you were assaulted by them, the police will likely not charge them unless their is compelling evidence. That said, even if they don't charge them, if you are concerned that you are in danger of future assaults, you can engage a lawyer to apply for an order restraining them from further contact with you, or alternately could install security cameras, etc on your property to ensure any such assault is recorded in future.
If the police haven't charged you on the spot, and you don't believe they will have any compelling evidence that you damaged their car, then you are unlikely to ultimately be charged, even though the police may give you some stern warning or similar.
I trust the above assists.
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