Thanks for the chance to help. I am an Arizona attorney with over 12 years experience. Hopefully I can help you with your legal question.
There is no law or regulation that will require the owner to give you a credit on your rent for electricity used to power AC.
That said, if there is a problem with the homes AC? If there is some problem with the AC unit, so that it is not operating as designed and therefore using more energy than it should? In such a case you can demand that the owner repair the unit...and if they refuse you can sue them for money you have to spend in order to pay the additional cost (based on its not working as designed)
Under the law, if you rent a home, you are entitled to have utilities (heat/AC) that work as designed. If the landlord is providing you a home with a faulty AC, that would be a basis to demand they fix it and let them know you will sue if they do not.
But you have the burden of proof
...I know that 2 story homes, in the Summer in many parts of Arizona, are notoriously difficult to keep cool (specifically the 2nd floor). So if this is a home design flaw (too many windows, not properly designed floor plans to reduce energy costs), that is not something you can demand they fix. But if the AC unit is not operating properly, you can demand that it be fixed
You may want to have a local technician to determine if it is defective (leading to inefficient operation). IF so? You can demand it be repaired or replaced. IF it is not defective, then you will not have recourse with the landlord
Let me know if you have more questions...happy to assist if I can