There has been a lot of discussion about this. I am building a brewing room in my basement as I pan to upgrade from the current 3 gallon set up to 10 gallons. My propane kitchen stove struggles to boil the 4 gallons or so already, so 10 gallons in the kitchen is not feasible. Outdoors is not an option as I would be unable to brew in Dec, Jan, Feb, Mar, and possibly April and to me not acceptable. I do not have a garage. I plan on using propane becuase the cost of the electric build is twice that of propane and propane will cost less to actually run due to the high cost of electricity in my area and natural gas is not available where I live. Propane can be used indoors safely but you must have indoor rated burners. My research indicates that the high pressure burners are not indoor rated (at least the ones I have found) and should be used outdoors only. Low pressure burners are rated for indoor use are more efficient in burning propane just not as hot (70,000 BTU from Agra-Supply). The room you use must have an exhaust fan capable of exchanging the air in the room completely once ever 5 minutes. I would recommend two fans one bringing fresh air in from outside and one exhausting air outside. Fresh air in vent must be higher than the exhaust vent. Since CO and CO2 and propane are heavier than air the exhaust vent must be lower but not at floor. 24 to 36 inches up from floor is good. Fresh air in is best at or near the ceiling. In vent must be fresh air from the exterior and the exhaust must vent to the exterior. Separate the outside vents as much as possible, keeping the exhaust downwind if possible for the prevailing wind direction. Proper research and planning are needed but propane can be used inside safely. A CO and CO2 detector are needed as is a Class C 4kg fire extinguisher. Also never leave a lit burner unattended and if you use portable tanks, remove them to the exterior when not directly in use.
I will be posting picture os brew room build very soon.