Your carbs. It sounds like your floats aren't closing one or more of your needle valves all the way. Could be some crud from the tank, could be worn needles, could be a bad float. It happens periodically with my 750 if I don't shut off the petcock when I park the bike. Always turn off the petcock when you park the bike. Always. To stop the flow without pulling and cleaning the carbs, like you probably should, try tapping on your carbs to try to vibrate the needle back into the seat when it starts to leak.
Patrick