I replaced the ice maker unit. It wasn't apparent that it was exactly the culprit because it continued to make ice. It appeared that too much water was going into the ice tray each time. This could lead to looking into the valve that fills the ice maker or the ice maker control board. I took a chance (as this was hard to catch happening) that the ice tray was not completely emptying during its cycle and that would lead to the overflow. That was the case and all is good now!