I live and work in Arizona for a business based in New Mexico. Do I owe state taxes in both states?

I currently live and do all of my work from Arizona for a business based in New Mexico.   I have been getting taxes taken out for both Arizona and New Mexico from my paychecks.  I have several questions about this:

 

1. Do I owe taxes in both states?  

2. Do I need to file a state return in both states?