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IRS.gov Website
Publication 17
taxmap/pub17/p17-117.htm#en_us_publink1000173204

Personal Property Taxes(p151)

rule
Personal property tax is deductible if it is a state or local tax that is:
A tax that meets the above requirements can be considered charged on personal property even if it is for the exercise of a privilege. For example, a yearly tax based on value qualifies as a personal property tax even if it is called a registration fee and is for the privilege of registering motor vehicles or using them on the highways.
If the tax is partly based on value and partly based on other criteria, it may qualify in part.
taxmap/pub17/p17-117.htm#en_us_publink1000173205

Example.(p152)

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.