The car that I hit was parked behind my vehicle.She wasn't parked directly but her left headlight was toward the center of my rear end . There is nearly no visible damage to my car but rather "scuff marks" on my tire. Her drivers side door at the front of her car has a small visible dent. I am fully insured but it seems that she is not. The cop said I could owe her up to 1,000 dollars but is this possible since she is not covered AT ALL?:mad:

You hit her! Whether she was covered or not doesn't matter. Even if it was, they would just go after you for reimbursement.

Just turn it into your insurance and let them take care of it, unfortunately uninsured motorists have all the rights of people with insurance. In some states, including California, there is a Proposition called Prop 213 where they cannot collect general damages (pain and suffering) but they are still entitled to get their vehicles fixed if they are not at fault for the loss.

Why on Gods green earth do you not believe you would owe her for the damage, Her having or not having insurance is not even an issue.
IF SHE hit you, then you would worry how she would pay you, but you are at fault, so you can either pay for her damage or turn it over to your insurance