Falsely accused of damaging car while uninsured.?

An elderly gentleman says I hit his car with my car door, the rent-a-cop wrote in the incident report that I did it based on his own opinion and not fact. There is no proof, no witnesses. The man has changed his story at least 4 times already just to make his claim viable. I was uninsured but I don't think that matters when I didn't hit the man's car. I live in Ohio. Do I have any protection? I don't have an insurance company to fight for me and there are no criminal charges. Legal aid so far can't help if this falls under traffic. And the public defenders office won't help because there isn't and won't be a court case. Is there ANYTHING I can do? I literally make $240/month on disability, I have a 17 year old car, and am a single parent. I can't afford to pay, and I mostly refuse to because I didn't do the damage and payment is an admittance of guilt. What do I do? Or what will happen?