What brand of carb is used on that bike?
A carb's float bowl has to be vented to the atmosphere and this open vent hole will be somewhere in the upper part of the carb body. Although fuel could be coming from the vent, carbs usually have some other provision for overflow... When the float fuel level gets too high, extra fuel might be diverted and could exit anywhere..
It sounds like the carb's float needle valve is leaking. The valve should stop fuel from coming in once the proper level is reached. If it doesn't the carb will leak.
The gascock or petcock wouldn't be at fault.. a carb is not supposed to leak when the fuel supply is turned on.