Hi - my name is XXXXX XXXXX I'm a Personal Injury litigation attorney. Thanks for your question.
You are not required to pay this and you can dispute the claim. Whether you want to do that depends on the specific facts of the incident.
If the accident wasn't your fault - at least not totally your fault, then you would have a defense to the claim; and it's good news if the officer that worked the accident didn't claim the accident was caused by you.
The problem is that if your insurance coverage doesn't involve bodily injury, it is very likely that your insurance company will not provide an attorney to defend you - - which means you'd have to either defend yourself or hire an attorney (which would likely cost more than what you're facing as a claim ($3000)).
If you believe that the incident was not your fault, then you may want to refuse the claim and see where it goes. It may be that the insurance company writes off the claim and doesn't sue; if they did sue, you could offer to settle at that point. If you think the accident may have been your fault, then you should ask for a copy of the medical bills, review them and make sure that the claim is legitimate, and then make an offer to settle. Chances are that the insurance company will take well less than the claimed amount.
Because you don't have insurance, you are really going to have to look at it from a cost prespective. If you don't want to run the risk of being sued, then it's cheaper to offer a settlement, pay it and move on with life.
However, if you think the bills are bogus, that the accident wasn't your fault, and that you don't owe anything, then you certainly can fight it, but it may be costly - time and money - for you as well.
I hope this provides insight to your question, but if you need additional informaiton, please REPLY and I'll be happy to respond. Thanks.