This is a new one on me. I would think the petcock is the problem, but the only way to be sure, is to remove the tank and bench test the petcock. Apply vacum to the petcock and look at the thing as you put it in the various positions. Gas will come out, so plan to catch it in some fashion. I would put a short piece of hose on the petcock and plug it up so you can see if the petcock is leaking. Could be the fuel line is leaking because of a crack, but I would think it would leak in any of the on positions. Does it leak with the engine off? Or only when running? Maybe the petcock O-ring at the tank is leaking. Did you have the petcock off the tank? Lots of reasons this could be happening, I would think. Only way to figure it out, is to get your hands dirty. Maybe someone who lives close to you could give you a hand. It would help if we knew where you live, to find someone close.
