Unplug the fridge and empty the freezer. Remove the ice from the ice maker as well. This gives you easier access to the ice maker and also allows the ice maker to thaw. It may be leaking because of excessive ice locking up the system and the problem may be solved once the ice is gone.
Fill a turkey baster with hot water and 1 tablespoon of baking soda. Use the baster to pour the solution into the defrost drain in the freezer. This helps clear the drain, and GE recommends it as a way of preventing or stopping leaking from the freezer and ice maker.
Plug the freezer back in and turn down the thermostat on the ice maker. See whether adjusting the thermostat in the freezer affects the performance of the ice maker. If it doesn't work, the thermostat itself may need replacement. Unplug the fridge again.
Inspect the ice maker and the ice bin to look for cracks in the plastic. Inspect the hoses as well to look for breaks or corrosion. If the ice bin is damaged, it needs replacement. Likewise, install new hoses if the current ones are causing the leaking.
Pull off the face plate on the freezer thermostat. Unscrew it from its housing with a screwdriver and unhook the wiring harness from the back. If the thermostat isn't keeping the freezer appropriately cool, the melting ice may lead to leakage. Replacing the thermostat corrects that problem.
Plug a replacement thermostat into the wiring harness and screw it back into position. Replace the faceplate. Plug the fridge back in and let the ice maker run to verify the leaking has stopped.