In Tucson they just plug into the OBD-II port and check readiness and function of the SES light. I imagine Phoenix metro is the same.
They also check the gas cap.
In my experience with my 1997 Cougar, 2000 Grand Marquis, and my fathers experience with his 2000 Expedition, they don't pop the hood, they don't look under it with a mirror, nothing. BUT in the link provided above, they MIGHT do a tampering check. I have not seen them do it on an OBD-II car, but all my pre 1996 cars they check them out underhood (and they even sometimes appear to know what they are looking for, but don't), entire exhaust system, holes in cats or injection tubes, etc.
97 Mark VIII LSC/Silver/Gray leather
97 Cougar 4.6 Sport/White Opalescent Tricoat Metallic /Gray leather down but not out?
89 Cougar LS 3.8/Oxford White/Gray velour/HG need replaced AGAIN
00 Grand Marquis LS/Vibrant White/Gray velour
63 Falcon 302/black and rust/shed isn't moving
82 F-150/Oxford White/dumb VV carb doesn't pass emissions