Did you get a police report?
I think that here in Westchester County, if the pothole has been reported prior to your incident,
the county is responsible for damages caused.
If the hole isn't reported and they don't know about it,
I don't think you can put a claim on it.
Either way, if you can get a cop to stop at the scene, after it happens,
and write a report, that is all the proof you really need.