Generally speaking, a propane heater should not be used indoors. While some propane heaters are labeled "for indoor use," there is still risk of carbon monoxide poisoning.
The Consumer Product Safety Commission reports that every year there are around 150 non-fire carbon monoxide poisoning deaths, mostly caused by consumer products like space heaters, propane heaters and generators being used in unventilated areas.
According to the Centers for Disease Control and Prevention, an un-vented gas space heater that meets current safety standards is designed to shut off if oxygen levels fall too low. But in Massachusetts in 2011, a propane heater with an "indoor use" label was blamed for the deaths of two residents due to being in a poorly ventilated area, according to a local news source.