Basically, most states follow the same rules the IRS does for this. If you owe taxes and haven't paid them, then you're not in the clear for 10 years. However, if the IRS owes you a refund, you have three years to file and claim it. If you file more than 3 years back and are owed a refund, you will not get it. So if your particular state follows the same guidelines you can only file 2013 to present if you're due a refund.
Additionally, TurboTax does not support their program more than 3 years back. So at this time you can only use TurboTax for 2013 taxes to present.
For your specific state of AZ, check the state's department of revenue website if you need to, to confirm they follow the IRS guidelines. Most likely, they do.