Uninsured motorist bodily injury coverage will pay for your injuries up to your policy limits in case of a hit-and-run or miss-and-run (where a driver is forced to swerve and has an accident). But uninsured motorist property damage (UMPD) does not pay for damage to your car. To make a property damage claim under your UMPD coverage, you need an identified at-fault driver so your insurance company can confirm that he or she does not have liability insurance. If you have collision insurance, on the other hand, you are covered for property damage from hit-and-run and miss-and-run accidents.