The accident occurring on private property normally does not make a difference to claims adjusters. It is the facts of the accident that will matter. In Michigan usually cars are not covered by the at fault person's insurance company and instead the vehicle's owner collision coverage.
However it sounds as if your car was parked. Property Protection (PPI) under Michigan's no-fault laws pays up to $1 million for damage a car does in MI to other people's property, such as building and fences. Usually other moving cars would not be covered but if the motorist hits a parked vehicle that that is covered.
According to the MI Financial and Insurance Services site, PPI does pay for damage your car does to another person's properly parked vehicle. So you may be able to place a claim against the other person's PPI coverage, if your car was properly parked. The insurance adjuster for their insurance company should be able to determine this.
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[Let CarInsurance.com help you find affordable auto insurance now.] If they decide that your car was not properly parked and thus not covered then you will only be able to recover the mini-tort amount of $500. This amount can be sued for from the at-fault party and is basically available to you in order to pay your collision deductible amount.
Under Michigan's mini-tort law, if you are 50% or more at fault in an accident you can be sued for up to $500 in damages to the other person's car that are not covered by collision insurance. For more information on this law contact your insurance agent. | 
