Yes, Arizona does restrict who can practice engineering!

from
http://www.azleg.state.az.us/FormatDocument.asp?inDoc=/ars/32/00123.htm&Title=32&DocType=ARS

Arizona Revised Statues
32-123. Application for registration and certification

(L00, ch 86, sec. 7)

A. A person desiring to practice architecture, assaying, engineering,
geology, home inspection, landscape architecture or land surveying shall
make application for registration or certification on a form prescribed by
the board, subscribed under oath and accompanied by the application fee.
If the evidence submitted satisfies the board that the applicant is fully
qualified, under section 32-122.01, 32-122.02 or 32-126, to practice the
profession for which registration or certification is asked, it shall give
the applicant a certificate of registration or certification, signed by
the chairman and secretary and attested by the official seal. If the
applicant seeks registration as a professional engineer, the certificate
of registration shall list the proficiency designation in the branch of
engineering in which the applicant has demonstrated proficiency.