This is a simple question that should have a simple answer, but a tangle of national and local building codes, energy codes, manufacturers’ installation requirements, and even the age of the building awaits the unsuspecting inspector, builder, or homeowner trying to decipher this question.
Let’s start with the 2018 International Residential Code.
This is enough to drive a person to drink. What starts with a straight and clear answer turns into Pandora’s Box once the exception is taken in. As I interpret this exception, you can install a vent-free fan that does not discharge to the exterior as long as you meet the manufacturer’s installation requirements AND as long as mechanical or natural ventilation is otherwise provided for the kitchen. I have seen an excellent example of this in a modern LEED-build condominium unit. The cooktop fan was vent-free and designed to simply capture cooking grease. Because the building was designed to use as little energy as possible, they wanted to exhaust all of the mechanical ventilation through the heat recovery ventilator. A cooktop fan discharging to the exterior would have short-circuited the heat recovery ventilator and a lot of conditioned air that would have been vented out through the kitchen cooktop fan to the exterior would have had to be replaced. To conserve energy, they installed the set-up shown below.
Some older buildings have similar arrangements where an old fan is installed in the exterior wall of the building and not necessarily above the cooktop. Obviously this does not include an HRV, but the concept is the same where the fan is not directly above the cooktop.
So, what if there is no exhaust fan or heat recovery ventilator located anywhere in the kitchen?
In that case it starts to depend on the age of the building. Residential construction built prior to the energy codes of 1991 may be able to use a window to meet the natural ventilation part of the exception. Older buildings were generally not as air-tight and so fewer requirements existed to provide mechanical ventilation. You see this in lots of ways; older buildings often do not have fans in the laundry room or even bathrooms. I do not recommend this configuration, but one could argue it is more of an improvement. My home inspection reports often refer to this as an improvement item when noted in older buildings.
If the house was constructed subsequent to modern energy codes and is generally newer than 1991, it should really have some type of mechanical ventilation located somewhere in the kitchen. It does not necessary need to be above the range but somewhere in the kitchen. The slide below is from the 2018 IRC mechanical ventilation section.
With all of this, your milage may vary. Requirements could be different in different climate zones and in different jurisdictions. The comment attached below is what I have in my report template. This narrative comes with ScribeWare as part of the Default Residential Template for writing home inspection reports. If I find a kitchen cooktop/range that has no fan or ventilation I typically refer to this as a repair item, but I can easily switch this to an improvement item if it is an older house and I feel that modifier is more appropriate.
I have taken this information from the Pacific Northwest climate zone. I hope this helps!