http://www.azdps.gov/Services/Concealed_Weapons/Permits/Obtain/
Eligibility
Applicants must:
be a resident of this state or a United States citizen;
be twenty-one years of age or older;
not be under indictment for a felony offense;
not be convicted of a felony offense, unless the conviction has been expunged, set aside, vacated or pardoned, or the individuals right to possess firearms has be restored AND the individual must not be a prohibited possessor under state or federal law.
not suffer from mental illness and been adjudicated mentally incompetent or committed to a mental institution;
not be unlawfully present in the United States;
complete a firearms safety training program pursuant to ARS §13-3112.N.
http://www.azdps.gov/Links/ARS/?l=13/03112.htm
ARS §13-3112.N. (N.) An applicant shall demonstrate competence with a firearm through any of the following:
1. Completion of any firearms safety or training course or class that is available to the general public, that is offered by a law enforcement agency, a junior college, a college or a private or public institution, academy, organization or firearms training school and that is approved by the department of public safety or that uses instructors who are certified by the national rifle association.
2. Completion of any hunter education or hunter safety course approved by the Arizona game and fish department or a similar agency of another state.
3. Completion of any national rifle association firearms safety or training course.
4. Completion of any law enforcement firearms safety or training course or class that is offered for security guards, investigators, special deputies or other divisions or subdivisions of law enforcement or security enforcement and that is approved by the department of public safety.
5. Evidence of current military service or proof of honorable discharge or general discharge under honorable conditions from the United States armed forces.
6. A valid current or expired concealed weapon, firearm or handgun permit or license that is issued by another state or a political subdivision of another state and that has a training or testing requirement for initial issuance.
7. Completion of any governmental police agency firearms training course and qualification to carry a firearm in the course of normal police duties.
8. Completion of any other firearms safety or training course or class that is conducted by a department of public safety approved or national rifle association certified firearms instructor.
As an aside: I'd already completed #5 & 7 but still had to complete #1 to get the AZ CWP. At any rate... I can't figure NM's problem.