Generally, car registration fees may be deductible on your federal income taxes,
but only under certain circumstances. The portion of the annual registration
fee that is charged based on the vehicle's value - as opposed to its
size, age, or other characteristics - can generally be claimed as a
deduction. If part of your registration is indeed deductible, you must
itemize your deductions to claim it, rather than using the standard
deduction.
As the Arizona "public safety fee" that you ask about is a flat fee, rather than value-based, it would not be tax deductible for federal income tax purposes.