Ice maker does not work. When on it leaks water that turns into icicles

There is an adjustment screw on the end of the ice maker which you can see when you pop off the cover on the end. It has a "-" and a "+" to tell you which way to turn the screw. Here is one model, but there are other styles almost identical that are simpler and have the water valve at the bottom of the refrigerator that I was referring to: https://dl.dropboxusercontent.com/u/8010163/Whirlpool%20%20Icemaker%20Ice%20Dispenser.pdf
https://dl.dropboxusercontent.com/u/8010163/Whirlpool%20Icemaker%20Troubleshooting%20Service%2 0Manual.pdf
The second manual is the one for the most common model that I was referring to, and on page 8 you will see the adjustment screw. Turn the screw clockwise to make less water go in. I would advise only turning it 1/4 to 1/2 turn at the time. These ice makers are used in almost all models of refrigerators as the refrigerator manufacturers do not make them but buy them from the company that makes them for all makes from what I can gather. If you cannot adjust it so that it does not overflow then you may need to check the water solenoid valve.