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The example below was extracted from IRS Publication 17 and makes the answer to your question very clear and shows that you can deduct that portion of the tax that is derived from the value of the vehicle.
Your state charges a yearly motor vehicle registration tax of 1% of value plus 50 cents per hundredweight. You paid $32 based on the value ($1,500) and weight (3,400 lbs.) of your car. You can deduct $15 (1% × $1,500) as a personal property tax because it is based on the value. The remaining $17 ($.50 × 34), based on the weight, is not deductible.
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From your vehicle registration, you should be able to find the weight of your vehicle.
1. Divide the weight by 100.
2. Multiple that amount by 0.50 to find the part of the tax that is based on the weight of the vehicle. Since this amount of the tax is not deductible, you can subtract it from the total tax bill to arrive at the deductible portion.
In the above example we had a 3400 pound vehicle; therefore,
3400/100 = 34
0.50 x 34 = $17 tax on the weight
The total bill was $32, so $32 - 17 = $15 which is the deductible portion of the tax.