Washing machine taps spring leaks as the valve stem, which is the screwlike piece in the middle of the tap's handle, loosens and allows water to leak. Over time, the packing material inside the washing machine's tap will break down, also allowing water to flow freely through the connection between the tap and the washing machine's water line, or through the middle of the tap's handle. Ultimately you'll have to replace the packing material inside the tap's valve to stop the leak.
Shut off all of the water in your house by turning the water shutoff valve.
Tighten the nut in the middle of the leaking tap's handle, using a screwdriver. Turn the water back on and inspect the tap for leaking.
Turn off the water shutoff valve if the leaking persists. Wrap plumber's tape around the exposed threads on the washing machine's tap.
Remove the tap's valve with a plumber's wrench and replace the worn-out packing material inside.
Find string valve packing material either at a plumbing supply store or a hardware store.
Overtightening the valve's stem can cause damage to the valve and the packing material inside. Do not turn the stem more than 1/8 turn.