Car or private liability. Who pays (if any)?

Hello together, unfortunately today, for reasons still inexplicable for me;-) (I just didn’t see it) a small staircase with my car drove down and of course put on the same time. As I said, I just did not see that there were three steps and there was no intention (possibly negligence). Ok, there was a smaller damage to the car of 100€, so that is not so wild. Unfortunately the stairs (foreign property of the city) is also damaged (the gens I don’t know about the damage yet), but I wanted to ask you before, if there is a car liability or my private liability for the damage on the stairs? I would like to avoid the car liability due to the upgrade, but have the fear that I will not come around. Is that right? Thank you for your help.