Remove the carburetor and drain out all the gas. Use carb cleaner to dry out the fuel inside and out once you remove the top. Set it on a dry piece of cardboard and carefully fill it 2/3 the way with fuel and watch the cardboard for leakage. Modern fuel is really bad about climbing walls and seepage, most likely it's its the top leaking, fuel will migrate up the walls and leak past the gasket and run back down the inside or outside of the main body. The screws you see leaking are just where it lands and leaks from. The main body doesn't have fuel ports or any hole from which fuel can get to the out side, it all has to go up to the top and out into the air stream, or up and back down fuel passage ways, either way it has to be drawn up. Too high of a float and too high of a fuel level makes the migration even worse.
My W1 carters will have fuel residue on the lid and screws, even though the fuel is well below them, fuel migration.
If you find no leak from the cardboard test, look for a wrapped lid, bad gasket, too high of a fuel level, or leaking float.
