Not a concern unless the OP is Korean.
A electric space heaters like these.
http://cms.srmi.biz/website//images/resize.jpg
http://madisonhomebuilders.net/wp-content/uploads/2014/11/11177107663_a3d135e122_z.jpg
Put out no CO unless it is burning oil or kerosene.
If it is electric not burning oil or kerosene there is no CO being put out.
If you’re running a generator which produces the electricity that runs the space heater, the aforementioned generator could have an upset and release CO that kills you… (hey, it could happen) 
Simple electric space heaters produce the majority of their heat thru direct radiation. Fancier ones with fans amplify this by heating and circulating the air via convection. If you put a radiant electric space heater in a giant glass bell jar and pumped out the air and turned it on, if you put your hand up to the glass it would still feel warm by being heated via direct radiation (in this case a fan would do nothing)…
You guys really beat this one to death. Nice job 
Interesting answer. I know that ventless gas fireplaces are becoming more prevalant and are used for some heating. I am not a huge fan not just because of CO possibilities but because of lots of additional H20 being added to the air. Potentially too much. And you shouldn’t use ceiling fan while they are on etc.
I wonder how the gas oven differs from a ventless fireplace when used in a house designed for a ventless fireplace. I’d assume the combustion process is similar but I don’t really know.
A properly designed gas fire should produce little to no CO. Production of CO is evidence of inefficiencies in combustion. (One might note that during the combustion of gas there is a lot of CO involved - it is what makes the flame blue) but once done, the products are ideally CO[sub]2[/sub] and H[sub]2[/sub]O. Some ventless heaters use catalytic converters, one would expect this to reduce the CO emission to very close to zero (once they are up to temperature.)
Where use of gas for heating has probably got a bad name is that town gas (as opposed to natural gas, or LPG) intrinsically contained a lot of CO. That was why it was possible to commit suicide with it. Now the normal gas supply could conceivably suffocate you, but it won’t poison you.
Ventless gas heaters always worry me none-the-less. Whilst they should emit close to zero CO, they still need a properly ventilated room to avoid build-up of CO[sub]2[/sub]. People do come to grief because of this.
Ventless fireplaces try to maintain an optimal flame that produces the least amount of CO possible. That amount is not zero. Properly installed they shouldn’t be any more dangerous than a stove, never the less, they have been banned in some states.
Thank you. We would have been done at post #8, but then in post #10 the OP asked for it. And we made sure he got it. 
For most people low levels of CO from electric heaters are negligible but there are people who have become CO sensitive due to chronic low level or acute high level exposure. For these people they have developed Multi-sensory sensitivity (MUSES). In which cases any stresser
Looks like the imaginary CO finally killed KBC76!
One and done. Makes for an awkward ‘In Memoriam’ post.
If the amount of CO produced by an electric heater is enough to cause you health problems, then you don’t have a physical health problem; you have a mental health problem.
I see we’re still gassing on about this.
It was the heat of the moment.
FWIW, the website linked to near the top of this thread has since been updated. It now says “Electrical space heaters pose no danger of carbon monoxide poisoning, unlike those that burn fuels, such as kerosene.”
If electric space heaters “produced CO” then what about all the other appliances that convert electricity to heat one way or another?
TV sets, computers, electric stoves, refrigerators, light bulbs (esp. the old incandescent ones) and on and on.
If there was a measurable bit “produced” by an electric heater, the total amount by all appliances would be huuuge. 
KBC76’s folk would have to pretty much abstain from electricity entirely. Even wires gets warm!
Flash news: electric space heaters produce enough CO to kill zombies. Like this one, hopefully. What a gas!
That’s silly. Those people probably are just suffering from an allergy to Wi-Fi.
Is my toaster going to kill me?