You should be able to make a claim with your neighbor's property damage liability coverages since they were at fault for backing into your legally parked car. You should obtain insurance on your car though as soon as possible so that you are not cited for driving without insurance.
According to the Drivers and Vehicles section of the Wisconsin Department of Transportation, Wisconsin does not have a no fault law instead they follow what is known as “contributory negligence.” This type of negligence law (Wisconsin Statute 895.045) states if it is determined you are more than 50 percent negligent in an accident you must settle the claim. The WI DOT also notes that an uninsured motorist is always considered more negligent than a passenger or a stationary object.
The at fault party's insurance company will tell you what steps you need to take once you call to place your claim with them.
We want to reiterate how important it is for you to get insurance on your car because if you caused an accident while being uninsured penalties in WI are quite severe.
Wisconsin enacted in 1945 the safety responsibility law to protect those who suffer damages in accidents caused by uninsured motorists. The program provides an incentive for motorists to carry liability insurance or otherwise satisfy accident damages. The law takes away the driver license and vehicle registration of uninsured motorists who do not pay for damages or injuries they cause.
When the WI DMV receives injury or damage reports, the accident report is reviewed to determine if the uninsured driver appears to be at fault. If so, DMV calculates a total for the damages, any injuries and estimated court costs.
The DMV sends notices of suspension to the driver who appears to be at fault in the accident. The registered owner(s) of the uninsured vehicle, if different than the driver, also receives a notice of suspension. A safety responsibility suspension remains in effect until the uninsured motorist complies with one of the safety responsibility requirements that the WI DMV lists on their site. Then the motorist must also go through a reinstatement process to get their driving privileges back.
To get quotes on Wisconsin auto insurance for your vehicle, click here.