My refrigerator is a Kenmore, side-by-side, and it’s leaking water from the freezer side. The leaking is not constant. Instead it occurs only occasionally. However, it leaves a puddle at the foot of my refrigerator that I have to wipe up a couple times a week.
Sounds like a plugged drain hose so the water from defrost is entering the fridge.
The following should help
http://www.applianceaid.com/frig_leaking.html
The drain tube can often be cleared with a turkey baster and warm water,
Compressed air also works.
Sometimes even a wire.
Also check that it is not plugged up with dust etc. at the drain pan under the unit.
If it looks like gunk is growing in the tube flush it with a 10% bleach solution. Let it sit 15 minutes, then do it again, then wait another 15 and flush it out with water. Just be careful to not overflow the drip pan.
I would also wear old clothes.
Probably a good idea to clean/check your condenser coils and the fan while you are at it.