In California, we need to have a vent (ducted or not) hood above the range. The bottom of the cabinet (if you are using one) should be 30 inches from the top of the cooktop, and the bottom of the hood should be 24 inches from the top of the cooktop.
I sell park models (mini mobile homes or large drywalled RVs, depending on your point of view) for a living (well among other things, but I digress), and the factory that builds them goes by some code requiring vented hoods above the ranges. I believe it's a state-by-state decision, but the factory just builds all to the strictest code in the nation currently on the books. It could very well be California's code (you know how picky we are!).
hth!
Kristine