If I deduct mileage expenses to maintain my rental property, do I need to allocate the property taxes for the car between my personal deductions and rental deductions?

I live in a state that charges a personal property tax for a vehicle. Let's say that personal property tax is $1,000. Let's also say that I put 10,000 miles on the car in 2016, and 25% of the time I used the car travel back and forth to maintain my rental property (2,500 miles). Do I need to allocate that $1,000 personal property tax between my personal deductions and my rental deductions? So $250 of the personal property tax would be allocated to my rental deductions (because the car was used for the rental 25% of the time), with the remaining $750 allocated to my personal deductions?