If your floor isn't level, your refrigerator won't be level unless you take the time to make it so. Keeping the appliance on uneven ground can cause the ice maker to leak. Many refrigerators have adjustable levels that allow you to raise and lower the feet. Consult your user model to find out whether your refrigerator can be adjusted in this manner. If it cannot, insert a small wooden shim under the lowest feet to even the grade and stop drips.
A leak in the fill tube that directs water to the ice maker causes dripping in your freezer. Look at the tube inside the freezer leading to the ice maker. If you see water on the tube, or dripping from the tube, you need to replace this tube. A pinch or crimp in the tube can cause a leak, so massage out the pinch to fix the tube. Because the freezer's defroster is often located near the ice maker, a leak in the defrost water drain can make the ice maker appear to be leaking. Examine the plastic piece for cracks, tears or other damage that could cause a leak.
A large leak from the ice maker generally indicates that a major component has failed. Ice makers tend to be inexpensive. If yours has a broken part that's causing dripping water, replacing the ice maker might be more cost-effective than repairing it.
When troubleshooting your ice maker, turn off the water supply to the ice maker using the shut-off valve under your kitchen sink. This valve is generally attached to the kitchen sink's cold-water valve with copper wire. If you don't see the shut-off valve there, check the basement.