The purchase of a personal vehicle, not used in a business, is not a taxable event nor reported on a tax return.
If your state requires that you pay a personal property tax for the vehicle (ad valorem) based on the value of the vehicle, that personal property tax would be deductible as an itemized deduction on Schedule A. However, the total of all itemized deductions would have to be greater than the standard deduction for your filing status to have any tax benefit.