You need to watch it closely to see where and when the water is coming in.
If it continues to drip from the fill tube then it may be leaking past your water inlet valve.
If it spills over the ice tray when it fills with water then the ice maker is at fault. You may can adjust the fill time if you can find an adjustment with a + & - sign. Look behind the ice maker cover on front.
Does the water just partially miss the ice tray when it fills. It could be blocked with ice in the fill tube because of dripping water inlet valve . or It could be misaligned. | 
Ice Maker 
