Check your ice maker to ensure it is not filled with ice that is melting. Ice is formed on a rack above the ice bucket or compartment. There may be some ice remaining in the ice rack that was never harvested in to the ice bucket. Remove the ice manually to prevent more leaking.
Self-Defrosting Freezer Compartment
If your refrigerator/freezer is equipped with a self-defrosting mechanism, the defrost drains may continue to drain water away from the freezer compartment for some time following the unit being shut off. Check the defrost drains and drain lines for signs of clogs that would lead to delayed draining. They are typically located in the back of the freezer compartment and can be accessed by removing the screen on the top of the drain.
Refrigerators work in much the same way air conditioners do. Air taken from inside the refrigerator compartment is blown across a series of cold copper coils filled with refrigerant. This cools the air and also removes humidity from the air. The humidity condenses on the refrigerant coils and drains in to a condensation pan. This water can remain in the unit for some time and will have to be manually removed from the condensation pan to ensure there is no additional leakage.
All water removed from the freezer via the self-defrost mechanism or drained away from the compressor after condensing on the refrigerant coils winds up in the condensation pan. The condensation pan holds water, which evaporates in to the air, aided in part by its proximity to the hot compressor, condenser and fan motor. When the unit is unplugged, the electrical components do not speed up evaporation, and the pan may overflow. Remove the front grill on your refrigerator and slide the pan out from its seating. Dump the water and wipe down the pan before reinstalling.