Me, my husband and my sister parked my car in front of the apartment and went out to have dinner. There was no car behind us when we left.

When we got back in an hour, there was another car parked right behind mine and it was pushing against the rear bumper of my car--it was physically pushing against it. And the paint got scooped out.

So we called the police and asked the police to write a report on it. However, the people who bumped into my car mentioned something about"no fault policy" and said I will have to pay my car and they will have to pay theirs.

Is it true, no matter whose fault it really is, I still have to pay to fix my car in NYC even when it's not my fault?

So what did your insurance agent tell you, when you called them about the claim.

Have you considered just sue them in small claims court for the damage

... the people who bumped into my car mentioned something about"no fault policy" and said I will have to pay my car and they will have to pay theirs.

Is it true, no matter whose fault it really is, I still have to pay to fix my car in NYC even when it's not my fault?

New York appears to be a "qualitative threshold" no-fault (http://en.wikipedia.org/wiki/No-fault_insurance)state.

As Fr_Chuck suggests, submit the claim to your insurer and see what happens.

Not the way I understand it. If damage is caused by another party, their liability coverage should handle it. So you get an estimate of the damage and submit it to their carrier.

The problem here is they will probably claim that they parked with enough room and you backed into them and then called the police claiming they bumped you. Without proof either way, their carrier may deny the claim against liability which means you have to put a claim into your carrier and the costs may not exceed your deductible.

No fault refers to medical claims, not property damage.

It means no matter which party was at fault YOUR company pays YOUR medical bills.

Otherwise - file with your insurance company. I think it will be a "wash."