It is common procedure to turn the gastank fuel petcock to off when the bike is parked. Mark M has already addressed the float bowl system, and fuel supply as the first areas to investigate. But, at the bottom of each float bowl is an overflow drain tube which connects to a stand pipe inside the carb bowl. It's function is to drain off fuel when the float bowls are overfilled, so the fuel doesn't flow into the intake runners, to the cylinder, past the rings, and into the bottom of the engine to polute the oil supply. You should check the tubes and the stand pipe for blockage that prevents them from proper function.
