Подскажите пожалуйста,если я покупаю машину у частного владельца должен ли я платить TAX?

Да, должен.

Private Owner
If you buy your vehicle from someone other than a dealer, within 20 days of purchase the
Secretary of State’s office must receive the following:
• Application for Certificate of Title, license plates or transfer of current plates.
• Properly signed Certificate of Title in the seller’s name.
• Payment of title/license plate fees.
• Payment of Vehicle Use Tax. This tax is based on the model year of the vehicle if the
selling price is less than $15,000. If the selling price is $15,000 or more, the tax is
based on the selling price. An RUT-50 tax form must be submitted along with the correct
tax payment. The check must be made out to Illinois Department of Revenue. If
you junk your vehicle, you are exempt from this tax; however, you must obtain a
Junking Certificate from the Secretary of State.