As of July 23, 2008:
76-10-523. Persons exempt from weapons laws.
(2) The provisions of Subsections 76-10-504(1)(a), (1)(b), and Section 76-10-505 do not apply to any person to whom a permit to carry a concealed firearm has been issued:
(a) pursuant to Section 53-5-704; or
(b) by another state or county.
CFP holders are still exempt from 76-10-505 (carrying loaded on a street)