There is a lot of controversy surrounding "vent free" appliances, including gas fired stoves and cooktops.
The issue is where do the flue gasses go?
In a perfect burning flame the only byproducts are water and CO2, but it's rare to have a perfect burning flame. Common sense tells me that unless you stick to a very strict maintenance schedule which would include cleaning the pilot, cleaning the burners, setting up gas pressure(s), and doing a combustion analysis, I would never trust a vent free appliance in my house around my family.
On the flip side, everyone with a vent free appliance, or any fossil fuel appliance, should have a good crbon monoxide detector in their home. But here is the catch... Many of the CO detectors on the market alarm well above the Personal Exposure Limit (PEL) for exposure. So you may be stewing in CO gases well above the PEL for days, weeks, or, months and not even know it.
I am personally against vent free appliances, because I see how lazy people get with their vented appliances, no way in hell they realize the dangers of vent free.