You do want to be aware of venting issues, but...
We use a propane ventless heater in our living room. You may have seen the "blue-flame" heaters advertised. I used to sell these. There is a 100 gallon propane tank outside.
There is no exhaust ducting or chimney and the heater is designed to shut itself off if the CO level rises (or the O2 level falls, which creates a hotter flame). Ours puts out 10-30k BTU and kept our house at 70 while it was -11 out. There isn't any wasted heat.
California is one of the few states that doesn't allow these (for no good reason that I can see).
It does make sense to have a CO monitor in the area. But propane burns very clean and our monitor barely registers above background.
Our propane tank also supplies a "tankless" water heater, BTW. Again it is very efficient and heats water on-demand rather than heating and re-heating a tank.
Both of these appliances use no electricity.
"tankless" water heater Do you need something at each source point (each shower, each sink, etc.?) Thanks much.
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.