The problem that you describe usually occurs in top freezer model refrigerators. It is normally caused by a defrost drain tube becoming clogged or frozen. Water will leak into the refrigerator when the drain system freezes up. Every time the unit goes into a defrost cycle, water will run down into the refrigerator, instead of down the drain. To clear the drain, remove everything in the freezer, so the back panel can be removed. First disconnect power to the unit. With the panel removed, you will see the evaporator coil and directly under the coil is the drain trough (pan). The trough will probably be full of ice that will need to be removed. With the ice out of the trough, you will be able to see the drain hole, which will be plugged with ice. Use hot water to clear the drain hole. Keep working the hot water into the hole and wiping the excess water. This can take quite awhile, depending on how deep the ice is. This will need to be done until you get a good water flow down to the bottom drain pan. With the drain system clear, water should stop leaking in the refrigerator. If you would like more assistance, additional details will be needed, including the complete model number of the refrigerator.
If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services
: Be sure to disconnect the appliance before performing any troubleshooting procedures. If you are not comfortable with doing any voltage checks or repairs that might be recommended, please contact a local service provider for repairs. Be aware that there could be sharp edges inside the appliance that could cause cuts or other injuries to yourself or others.
I hope this helps.