My top freezer Whirlpool refrigerator (ice maker not hooked up) is getting water on top shelf and icing up. Also, water in crisper drawers.

Connie; give it a try, nothing to loose

You just need to take it apart to see the exact issue.

The most common problem is the defrost drain hole is plugged or frozen over.And the defrosted water from the evap coil is leaking in the fridge compartment,You may have to remove the back panel in the freezer compartment and defrost the evap coil and drain area.

This is not a major repair and also a very common problem. You will need to turn unit off and remove everything from inside the freezer. After this remove the back panel of the freezer and you will see ice built up at the bottom of the coils. You will have to remove all this ice and clear the defrost drain trough and tube. After the ice is removed you will see the defrost drain located about midways. Use a hair dryer to melt this then take a cup of very very very hot water and pour a little in the tube. Let stand for 5 minutes then dry it up real good and repeat. Do this till the drain clears and water flows freely. Then reassemble and you are good to go.

A common problem. All modern refrigerators have an automatic deicer. The heater kicks in, then MELTS the ice in build up in the freezer for a short period before freezing again. This water drains either in the fridge or out the back to the catch tray. Simply pull out the bottom drawers and clean the clogged drain hold where the water can drain and evaporate in the catch tray as it is designed to.

the defrost drain in the freezer is clogged with ice.
empty the food from the freezer, and put through a defrost. you might have to help the fridge defrost with a hair dryer. you may also have to remove the rear panel (inside the freezer) or pending on the model to bottom panel of the freezer.. (usually held in by 1/4" hex screws.)
melt all the ice, and be sure that the drain is clear, and it should work.

clogged drain line

Has the refrigerator got a wet inner back?
Ff this is wet, adjust it until this solid ice 'blobs', bt not encrusted, like in a freezer
The refrigerator may not be cool enough and the natural warm moisture allowed into the cool compartment when the door is open is condensing into fluid before it is cooling sufficiently to suspend the moisture as a vapour. If the cool compartment is cool enough, any warm air admitted ill be chilled before it is allowed to condense, keeping the refridgerator dry.
However, the only drawback is that you will have to monitor it to prevent the build up of excesive ice.
Also, whether the refridgerator is either empty of full willaffe the day to day operation.
Hope this helps.

YOUR DRAIN FROM FREEZER TO DRAIN PAN IS CLOGGED,LOOK INSIDE TOP BACK OF REFRIG. SHOULD BE DRAIN HOPPER,REMOVE AND CLEAR OUT DRAIN,THANKS-MIKE

pull the funnel tube out of the back wall and clean the drain that goes out the back wall of the refrig section