My question involves a careless driving and failure to report accident tickets from the State of: NJ

A car was parked and I inched up as close as I could get w/o hitting the car (or so far as I believe - ie., I did not feel anything and when I went out to check I was at least 1-2 inches from the bumper and then reversed another few inches and parked).

When I got back to my car (after taking son to Karate), there was a police officer there - I thought he was giving me ticket for parking violation (b/c about 8-12 inches of my car was past a sign for no parking). Instead he said I was in an accident and didn't report it. He said I had hit the car in front of me. I insisted I hadn't and explained what I had done. Seemingly he had his mind made up after talking to the driver of the other car (who was not the owner of the car and wasn't indicated on the accident report and who was no longer there when I came back) that it was I who hit her and not her backing up into me (simply b/c my license plate lined up with the slight damage on her bumper).

Can I really be convicted of careless driving and failure to report? Please help!