Really, that depends how you're asking it.
I believe, in terms of recording yourself on the census and other things, one only has to feel like they should be considered native american to make it okay to place it there. To my understanding, if you want to refer to yourself as a native american you can.
In terms of actually getting registered with tribes, I believe there's various blood quantom regulations as well as typically requirements with regards to your connection or relationship with tribal customs. I believe these vary by state and by tribe.
I don't believe there is any universal official standard across the board for how one could "officially" qualify as native american. Typically one must be recognized by one of the 500+ federally recognized tribes to be regarded as native american in a legal type of sense.
Personally, I always respected and felt that the notion of adhering to the culture...rather than just blood...was of utmost importance. I'm somewhere between 1/8th and 1/16th (My grandfather, who died while my mom was younger, was said to be half mohawk...but I know blood lines can be muddled) but I'd never suggest that I'm "native american". I didn't really learn that until I was in my high school years, I've never been significantly involved with the culture/heritage, etc. I believe if I really wanted to, I could track the information down about my great grand parents and try and begin a process to get a CIB and certified under the Mohawk tribe but frankly I'd feel that'd be more disrespectful to my grandfather's heritage than NOT doing anything since it hasn't been, nor likely would be, a significant impact upon my life and heritage.