Legal Question in Criminal Law in Arizona

The short answer to your question is yes. If they have evidence that you stole stuff they can charge you with a crime, they don't have to catch you red handed. Also it is irrelevant that you might have stolen the property in another jurisdiction. Once an Arizona officer is sworn in, they can make arrests throughout the State.

You should stop stealing stuff. It is unlikely that they are monitoring you to see if you will steal more stuff, but, morality aside, it is not a good idea for your own self interest. Multiple offenses can quickly become felony charges.