You definitely did the right thing by getting the police involved and getting the at-fault person cited. It typically does not matter that the car is registered in another state; it just means if they live there it might be harder to contact them in the future. You will need to find out if the at-fault person actually has insurance or not. Just because they did not have the proof in the car does not mean that the driver or vehicle is not insured. If the driver or car is insured contact their insurance company.

If the at-fault person does not have insurance you can get your insurance company involved if you have uninsured motorist property damage coverage. If you did not have this coverage but instead have collision your insurance should cover your vehicle damage up to its actual cash value minus the deductible amount you will have to pay.

If neither of these options applies, you will most likely need to seek legal advice to see if you can take the at-fault person to court to be reimbursed for your repairs. If you did have insurance to cover your repairs but had to pay a deductible you can request the at-fault person pay that.