I doubt any schools will ask you to prove your NA heritage, or ask what percent NA you are. The 2000 census definition of Native American is:"Persons having origins in any of the original peoples of North and South America (including Central America), and who maintain tribal affiliation or community attachment."If you feel you have a "community attachment", and have in the past identified as Native American or part NA, I think you can check the NA box in good conscience. If anyone asks you to "prove it" (again, I really doubt this would happen) just be honest.However, if you've never identified as NA until the law school applications process, that will look bad and could cause concern about your character and fitness. Only if you find yourself in this situation would I recommend DNA testing, historical research or something that can legitimize your choice to identify as NA now.
However, this would be my personal litmus test - if it didnt matter (basically, if there were no AA or benefit to doing so) would you still check the NA box? If you would check the box even if it wouldn't help you, then I say you are justified in doing so.