I had a similar problem with a freezer-on-top style Samsung. The solution to that was to defrost the freezer, remove the false backing plate in the freezer (required removal of the ice cube tray. the panel just pops out with a bit of pulling). The drain hole beneath the freezer coils was blocked with ice. This drain passes down into the fridge and then out the back of the fridge into the evaporation pan next to the motor. There is a collector pan under the freezer coils, this and the drain hole were filled with ice. When the freezer goes into its self-defrost cycle the water collects here and then overflows into the fridge.
I removed the ice with hot water/vinegar mixture (so it doesn't re-freeze immediately) and simultaneosuly used a bit of chiselling with a screwdriver to clear the drain plug. I did this from inside the fridge working up the drain hole into the freezer. The whole job took about an hour.
Bob, October 2010
