Construction Company Contracted By Employer Scratched Car

Hi all,
I'm looking for some advice on how to navigate this situation.
My wife is a teacher for a public school in PA. The school has been doing a large-scale renovation project for the last couple of months, both interior and exterior. Last week, my wife borrowed my car for work because I had to take her's to the shop for a repair. She called me that afternoon while still in the parking lot saying that there was mud all over the front of my vehicle (and several others), which she believed was from the construction. To her knowledge, no notice had been sent out regarding parking warnings or restrictions, so she had parked in the faculty lot where she always does.
When she got home, I inspected the car and there was hardened mud / dirt all over the bumper, hood, windshield, etc. I took pictures, and then hose washed the dirt off, which is when I noticed a handful of small paint chips. I take very good care of my car (garage kept, frequent washing / detailing, regular maintenance, etc), so I'm positive that these paint chips were not present prior to this incident.
The construction company would be the one responsible, and not the school, correct?
Who do we contact first about the incident? The school? Our insurance? We don't know the name of the construction company, so I would think we'd have to speak with the school first either way?
How would be prove that the paint chips were caused by the construction? Note: the week before a similar incident occurred, but my wife was out of the office. Other faculty members had said / complained that there was dust and dirt on their vehicles from construction, although as far as we're aware there wasn't any damage reported.
I assume it would help to have a video of the incident, which I think the school should have. Are they under any obligation to provide it to us? Is there any way for us to obtain it?
Anything else I should know about how to handle this?
This is my first time dealing with something like this, so I appreciate any help or direction!
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