According to my wife who is a licensed agent for a major carrier here in CT, the words "supplemental heating appliance" come into play. Boilers and furnaces are considered primary sources so they could care less. Stoves however will require notification as they are considered supplemental. They may want to look at the install, have the Fire Marshall look at it or possibly just make a note on the policy. If you screw up and burn the house down, they'll pay. Your life insurance carrier may have an issue if you die of CO poisoning so make sure you've had the policy beyond the six month to two year exclusionary for suicide.
The words "solid fuel appliance" will have the Fire Marshall itching to see it, he wants to make sure that he doesn't have to send apparatus to put your house out when it catches on fire or the coroner to remove pink bodies if you kill yourself with CO.
Last but least, the building dept will want"cash or check" for a permit.