Several months ago, I pulled out of a parallel parking spot and lightly bumped the car next to mine. When I looked in the mirror, I noticed that there was a smudge or scrape (I couldn’t tell which) on the mirror of the other car. I don’t know if I was the one who did it and, if I did, I don’t know how much damage it was. I also have no idea who owns the car and would have no way of finding out. I am wondering if perhaps I should put an advertisement in the local community newspaper to find out if anyone remembers having such damage done to their car. What should I do?
According to the Chazon Ish (Bava Kama 6:3; see also Nesivos Hamishpat 340:3; Shach 95:18, and other commentaries to Shulchan Aruch 95:6), and the common ruling of contemporary poskim, a person who causes such damage (a scratch) will be obligated to pay for fixing it.
This is true even though the actual damage is less than a perutah. Because the car will not be replaced, but the damage fixed, the person who caused the damage is liable to pay for fixing it (the same applies for soiling a suit, and similar damages).
Because it is fairly probable that you caused the damage (brushing against another car is likely to cause the type of damage you saw), you should try to locate the person involved, and placing an advertisement in the local newspaper seems the logical way to try.