Can I run a propane generator under my house?
CO production is certainly one concern, and you'd need to ensure that the exhaust system is properly ducted away.  

But equally important: any fuel-based generator (internal combustion engine) is a major fire hazard and should be placed something like 2 meters away from any structure -- in all directions.  I do not know the local code where you live, so that number may be different, and quite probably a non-flammable material may need to be placed covering  a wall between the generator and the house proper.  

All in all, for the cost of a few dozen meters of power cable, I would recommend installing away from the house and running a conduit into/thru your crawlspace.