The co levels seem to depend more on the stove then the fuel. It may be a function of flame front temperature or burner efficiency, but I'm no chemist.

http://www.bushwalking.org.au/FAQ/FAQ_Monoxide.htm

If you want to be double safe, co detectors are pretty cheap (<$30). I've got a pair of Kidde detectors in my house. One next to the furnace, and the other next to the drier. Both are gas powered appliances, and potential sources of co poisoning.
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