Grounded conductor can be smaller than 3 AWG. Larger of 250.122 or 250.24 C. For services some would say 2 trade sizes smaller than ungrounded conductors
The grounded conductor (aka neutral) needs to be sized for the calculated neutral load. If the calculated neutral load isn't significant enough to govern its size, the minimum size is the EGC size per 250.122 when it is a feeder, or when it is with service conductors ahead of the main disconnect, sized per 250.54(C).