I just want to chime in on this one. Propane does burn very clean. Very little CO. However, I've found that depending on the unit and how it's metered, the level of CO varies wildly.
I have a rather sensative CO detector that I use at work because of some of the projects I work on. I also have a Nighthawk CO detector that is in constant use in my house. I've found that my MR heater on the propane tank produces almost ZERO CO but at a max of 12K BTU, that's not a big hit. A Redi-heater, 40-55k BTU produces SO much CO that you can't use it in an enclosed space for more than about 15 minutes. A Promat 10t, 40K BTU heater is a vastly better heater, producing very low levels of CO.
Definately test your heaters, but Propane can be used indoors and unvented if you monitor it. Of course, don't take my word for it. Definately don't get a propane heater if you aren't willing to spend the money to have a proper monitering system. Built in CO detectors on some good heaters are the best option.
Propane is certainly better about that than, say, kerosene. But it still has lots of potential for danger when used indoors, and not just from CO2.