What would cause a sudden drop in humidity in my home? I have a ventless propane heater newly installed in my home, which has been an increasingly source of paranoia for me (constant condensation on the windows, worries about carbon monoxide poisoning).  It's been a interesting few weeks of trying to find the right balance of windows to crack; needless to say I'm looking for a new heater. 
Today, I noticed that NONE of my windows had condensation on them, even though the heater had been running for hours and the relative humidity outside was 100% (~30F) with fog and sleet.  I would expect it to feel like a swamp in here.

Now for the chemistry question- I know that the incomplete combustion of propane in a low oxygen environment would produce carbon monoxide, but is it typical for the air to become more dry as well?  Does the lack of oxygen also produce less water, and maybe more H2 or something like that?  What would cause the unusual drop (or perceived drop?) in humidity in my house?
the humidity is caused mainly from sources of water in your home such as plants, pets and of course humans. As you breath out water is coming out of you. And the condensation of water on windows is caused by different temperature outside/inside especially at the interface glass/air.
There is no way that heater can reduce humidity in sealed room (in means of decomposition of water as you suggested). Imho if you have CO alarm you have nothing to be afraid of.