Sounds to me like a bad water valve (controls water going to refrigerator located on back of fridge). wear and tear on the valve causes dirt and grime to collect on the inner parts and the valve does not shut completely which causes it to slowly leak which overfills icemaker. if part is left unreplaced the valve could stick open which would flood your kitchen (had warned a cust about this when i used to do appliance repairs and decided not to fix against my advice and cust called back the next day saying their kitchen had flooded)