I just changed out my single tank regulator with an auto changeover, 2 tank regulator. The pigtails that I installed both had inverted flair fittings. The regulator itself had tapered pipe threads where both pigtails attached. The regulator manufacturer also included the adapters need to go from the pipe thread to the flair end of the pigtails. The installation instructions specifically stated to use yellow sealant tape or pipe dope on the pipe threads. They also instructed to NOT use any sealant or tape to the flair attachment.
If you want verification, do a google search on how to seal pipe fittings.