Water Leaking Into Bottom Freezer?

I have a Kenmore model 596.72003011 bottom mount refrigerator. There seems to be water leaking into the freezer compartment from some where? When it gets into the bottom there it forms an ice lake. After about 3 days the ice lake reaches the seal and then the units begins to leak water onto the floor from the melting ice. The ice maker functions properly, the water dispenser works fine, the leak is not apparent at the filter. The water can be seen leaking at the bottom of the coils at the back of the freezer section just below the coils. When I turn off the water supply to the unit the leak stops. There is no apparent accumulation of water in the refrigerator section of the unit. Any ideas where the water leak may be?