Carbon monoxide is produced by devices that burn fuels. Therefore, any fuel-burning appliance is a potential CO source. Electrical heaters and electric water heaters, toasters, etc., do not produce CO under any circumstances. Assuming you are asking for ordinary circumstances, no.
Consequently, is it safe to heat the house with an oven?
A properly tuned oven should put out no more than 50 when door is closed. It is possible to have carbon monoxide poisoning from an oven that has its door open. So, I can say with confidence that is never safe to heat your home with a gas oven that has the door open, even a crack.
Do ovens have carbon monoxide?
Deadly carbon monoxide gas is given off from the gas flame that heats the oven. All gas stoves and ovens produce carbon monoxide, but that doesn't mean they have to be dangerous.
Do gas ovens emit carbon monoxide?
The electric elements in electric ranges do not produce combustion pollutants. Burning food produces smoke and carbon monoxide, and can cause smoke detectors and carbon monoxide detectors to alarm. So can self cleaning ovens during the clean cycle.