Fire Places can put out Carbon Monoxide and lead to Carbon Monoxide Poisoning if the wood you're burning in the fireplace is doing more smoldering than burning.
Make sure you have dry, seasoned wood that burns good without producing much if any smoke into the house.
If your wood fireplace is allowing smoke into the house from the fireplace then it likely that the firewood isn't seasoned enough or you have a downdraft coming through the chimney.
Most times though Fireplaces are very safe to use but it still would be a good idea to have A carbon monoxide detector in your home just to be safe.
Furnaces, gas water heaters, oil furnaces etc all produce small amounts of carbon monoxide and if not vented properly could lead to carbon monoxide poisoning and you'd never know it without a carbon monoxide detector.