Generally, no.  There's one exception for certain exempt backcountry food establishments.
"The local health officer shall accept food hander permit issued toa backcountry outfitter by the United States Department of Interior, or by a public health authority in Arizona, Colorado, Idaho, Nevada, or Wyoming.  This applies only to food handling done at a backcountry food establishment that meets the exemption requirements of Section 26-15a-105(1)(i)."
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