A number of things could cause this but first you do want to isolate the area that it is leaking from. If the fuel valve is leaking, your best bet is to replace it, same with the fuel line. Fuel line tends to get hard and can crack or not seal well with age. This is especially true if imitation fuel line is used. And believe me a lot of dealers use standard poly tubing as it can be bought for less than 5 dollars per hundred foot length. If the carb is leaking you could have a worn inlet needle or seat or it could be just dirty or varnished up. The float may have become dammaged or it might have a hole in it. Another often overlooked cause of fuel leakage is that the vent for the carburetor bowl is obstructed. In any event you should always turn the fuel valve to the off possition when the moped is not running and as long as the valve works, you should get no or little leakage.
Btw. What make and model moped have you got.
The Moped WareHouse of New Jersey