Can I be a resident of one state and work in another?

Yes, if you still consider yourself a Texas resident and are there for work, you would file a nonresident return for the income that you earned in Arizona.  You can use whichever address where you get your mail.

Most states in the United States define “residency” based on a person’s “domicile.”  Domicile, in general, is the place which an individual intends to be his or her permanent home and to which such individual intends to return whenever absent.

An individual can only have one domicile at a time.  Once a person acquires a domicile, he/she retains that domicile until another is acquired.  A change of domicile requires: 1) abandonment of a prior domicile, 2) physically moving to and residing in the new locality, and 3) intent to remain in the new locality permanently or indefinitely.  If a person moves to a new location but intends to stay there only a limited time (no matter how long), their domicile does not change. 

As indicated above, the location of a person’s domicile is dependent on a person’s intentions.  Intent is a state of mind.  A state of mind is difficult to prove.  As a result, taxing authorities (and courts) look to a person's actions to determine their intent.  Some of the factors that courts and taxing authorities look to include:

• Amount of time you spend in one location versus another
• Location of your spouse and children;
• Location of your principal residence;
• Where your driver’s license was issued;
• Where your vehicles are registered;
• Where you maintain your professional licenses;
• Where you are registered to vote;
• Location of the banks where you maintain accounts;
• Location of your doctors, dentists, accountants, and attorneys;
• Location of the church, temple or mosque, professional associations, or social and country clubs of which you are a member;
• Location of your real property and investments;
• Permanence of your work assignments in a location; and
• Location of your social ties.

OK, one follow up question about what state to say I lived in on December 31, 2016. I was technically in Arizona at that time in the house I rent a room in, but I left my vehicle's Texas registration and I kept my Texas drivers license. So, should I say I lived in Arizona with my previous address being Texas and note the date I "moved" to Arizona, or say I lived in Texas all year?

You should say you lived in Texas all year.  I think that question could be worded differently like "What state were you a resident of on Dec 31?" but Turbo Tax asks it to determine which states you need to file.  In your case, you know you have to file Arizona anyway, but you are not a resident.

I want to go to college in my home state, because it is cheaper. But i want to work in a different state. Can i do that?

I want to go to college in my home state, because it is cheaper. But i wish to work in a completely different state. Can i do that? And how? Would i just have to do the residency in the state i want to work in?

where can I get windshield sticker and smoke test of Texas residency for my car when I work in Indiana?

@hnguyen2021h We are here to answer income tax questions.   We cannot help you with your question.  If you live in Texas you will have to ask the department of motor vehicles in TX or if this is a law in IN then ask the DMV in Indiana.