Water drips down from Freezer. The wat...

Since you said the water supply is shut off, the likely culprit is a clogged drain tube that connects the defrost tray to the water collection pan for evaporation at the bottom of the fridge.

The source of the clog is usually either mold growth or more likely, ice build up. Regardless of which, if you access the defrost heater in the freezer section, you can thaw ice that has collected in the tray and if needed, use a turkey baster to direct a hot stream of water at the point the hose attaches to the tray and treat the hose for mold, below.

Once cleared of ice, mix a small amount (5 or 6 oz) of water and 1/2 to 1 ounce of bleach and direct down the tube to kill any mold / growth. Be careful not to use to much or overflow, as clean up will be difficult due to the bleach mixture.

The next thing to do (if icing up) is to determine why. A careful check of the defrost circuit should be done. Otherwise, you'll be doing this over - and it may start to affect the temperatures in the frozen and fresh food sections of the fridge.

I hope this helps!