I think the standard minimum to a hood is 24". Personally, I'd call the range manufacturer just to be sure.

The NKBA Guidelines state 24" to protected surface, 30" to unprotected surface (however, I think manufacture guidelines override these):

I think some of the manufactures make the clearance higher (not sure if the extra margin comes from their engineers or their attorneys). Is the range in question a typical model or is it a BlueStar or Wolf with multiple 20,000+ BTU burners? That's going to matter also -- but since you say its recirculating I'm hoping its a typical model.

The previous owner of our house put in an over the range convection microwave that has 17" of clearance above the cooktop. It is almost unusable (and probably unsafe).

It's a lovely but not über-powered Samsung nx58h9500ws -- so we are currently at a 23" clearance. I'd rather not have it so high that I see the lights themselves, but hmm. The reason I am currently stuck with it is that I have a 30H cabinet above it; others are 40H, thus leaving 10", less the height of the hood.

The specifications on my GE range are identical to the NKBA guideline that Benjesbride posted: 30" min. to a cabinet or other combustible surface; 24" min. when the "bottom of wood or metal cabinet is protected by no less than 1/4” (6.4 mm) thick flame-retardant millboard covered with no less than No. 28 MSG sheet metal (.015” [.38 mm] thick), .015” (.38 mm) thick stainless steel, .025” (0.64 mm) aluminum or .020” (0.5 mm) copper."

Say that three times fast. :)

Just to be double sure, I called GE customer service to confirm that a metal vent hood in fact falls under the 24" guideline. It does.

Our Zephyr hood specifies the same numbers, 24" to 32" over the cooking surface, if I recall correctly.