Typically if you are the one backing up when a collision occurs though you are the driver found to be responsible for damages sustained in the accident due to improper lookout. In some states both drivers may be found to be partially negligence and thus both partly at fault.
If the police came and made a report of the accident, this may also help decide fault. Ultimately for claim purposes the insurance companies involved will investigate the accident claim, get statements from each driver and determine who they find at fault or if they find both drivers to be at fault.
In many states and provinces, when an accident occurs the insurance companies involved will send out insurance adjusters to determine the extent to which you are covered and the degree of fault of each driver. Being a parking lot accident many State and Canadian insurance companies determine fault to be 50/50 unless there are extenuating circumstances.
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[Let CarInsurance.com help you find affordable auto insurance now.] For example in Ontario, Canada, Direct Compensation-Property Damage (DC-PD) is part of your mandatory coverage. Under a DC-PD claim you can recover for damages to your vehicle up to the extent that you are not at fault, less the deductible. For example if it is determined a 50/50 accident, your insurance company will pay 50 percent of your loss, minus your deductible. | 
