HOA's Gate Damage

I recently had an incident where the front gate to our community, which is all electronic, without a gaurd, came down on a truck I was driving to move my furniture. The gate arm came off of its bolts. I returned the arm to the front gate. Later a woman come to take my information. Being cooporative, I gave it to her. Now, several weeks later, I received an invoice charging my account for the repair of the gate arm. The invoice came with a letter explaining that the incident had been caught on camera. Since the gate arm came down on my car, as I'm sure the camera will show, am I responsible for damages incurred by the gate itself? Luckily there was no damage to my vehicle. Am I out of my rights to request access to the camera recordings? Also, per the invoice they replaced the arm, which was undamaged. Am I laible for all these charges, even if they are unecessary? Every time I drive through that gate, the arm is broken or damaged in one way or another. I find it hard to believe that they bill everyone this amount everytime any incident occurs. Please help? I would greatly appreciate it.