Your talking about a ductless central air or mini split. Its my understanding the cable that goes from the out door unit to the indoor wall mounted unit should have a wire in it to power the indoor unit. Also most units don't allow over 64 feet from outdoor unit to indoor wall unit. I could be wrong and the one guy who would definately know is hvac doc but i haven't seen doc around in a while.
The units that I have seen draw power from the inside unit. Could you post a photo of the one you have? I deal with quite a few of the National and Mitsubishi units here and they all seem to wire up the same.