KiDa, gray water may almost universally be pumped over the side in the U.S.
At the present time there are no Federal regulations on it. Only a few lakes, reservoirs and impoundments ban the overboard discharge of gray water. Lake Champlain and Lake George in the upper New York/Vermont/Canada area are the only ones of note. There are a few others, but their locations escape me at the moment - but they're smaller and less-known than Champlain and George.
Going one step farther, just for general info, there is no current technology available for the treatment of gray water that can be used on small boats (smaller than commercial ships). You can rest assured that if that technology were currently available, considering the fools in Washington and the various state legislatures, the discharge of gray water would, likewise, be banned. The detergents and fats that are in gray water, are not compatible with treatment systems for black water (sewage) and the two types of water may not be mixed before going to a black water treatment system - or the black water treatment system will be ruined.
In areas where the overboard discharge of gray water IS banned at the present time, it must be collected and stored in its own separate holding tank, then pumped out via its own deck fitting, at a dockside facility or pumpout boat. What THEY do with it once they have it, I have no idea.
That's the situation in March, 2011. However we never know what evils may be lurking about in the future.