In the state of Arizona, is is legal for my supervisor to falsify my time card?
It is NEVER legal for a supervisor to "falsify" your time card, even if s/he is trying to "help" you (perhaps by punching your card to reflect that you reported to work on time, even though you were late). Usually, managers change time cards to eliminate time that you actually worked, and therefore avoid paying you properly for that time. You should contact the Labor Commissioner immediately, and the people there will help you file a claim, if that is appropriate.
Employment / Labor Attorney
No. The federal Fair Labor Standards Act also requires accurate record keeping of time worked.