According to my information, neither the state of New Mexico nor the state of Arizona allows mandatory direct deposit.
However, my information is three years old. It is not impossible that one or both states may have changed their laws. You should confirm with the respective state DOL's.
If it should happen that one or the other state has changed their stance, the employer is bound to follow the laws of the employee's home state. Let's say, just as an example, that New Mexico has decided to allow forced direct deposit. Employees in New Mexico could be mandated to have direct deposit, but employees in Arizona could not. The same would be true, in reverse, if Arizona had decided to change their law since my information was published. It's not a one-for-all question; it is state specific.