The requirement for being an American is citizenship.
The criteria is needed by those who might want to be accepted.
That's true only in one context. I assume that immigrants most often are considered American as soon as they get their citizenship, but this is not the case in all countries. You might have a citizenship, but don't know the language and don't mix with the society in general. You might yourself feel that you are closer to a different culture because you know more about it. There might be a difference between a formal definition and an informal.
Another way to see it is: are you old? The answer depends on the context. You might be considered old in one context and not in another. (There is only a specific definition when needed, for example if you can retire or not.)
But ok, if it is possible do define criteria for who is Deaf, I am curious to read. I didn't mean to disturb the discussion, sorry.