Our GE side by side fridge, is leaking water, from the bottom of the icemaker trim, down the outside of door.
Icemaker is not hooked up.
Any ideas?

I had a similar problem a slow water drip through ice chute. Occasionally started spewing ice cubes by itself uncontrollably.
I have a KitchenAid Side by Side Built In Fridge Model KSSC48QVS02.
It appears the slow water drip shorted out the ICE dispensing pad which resulted in the spewing out of ice. The only way to stop it was by turning on the Holiday Mode which shuts down the ice making/dispensing functions of the Fridge.
The reason for the slow water drip was that the chute door was not sealing the ice chute completely and some air was getting in slowly melting the ice. The chute door was not sealing because the motor assembly was worn out so the motor would not push the door with enough force.
To fix it I replaced the Chute Door, the Chute Door Motor assembly and the shorted out dispenser pad. About $150 total. It took me maybe 1/2 hour to change the parts and 5 or 6 hours to figure it out and order the parts etc.
3 days later it seems a success and no more leaks of water or ice.....