It's not a star on the flag.
It's also not its own country. If it was, it wouldn't be sovereign to the United States.
It's a District, as delegated by the U.S. Constitution. It's not governed by any state law - only federal law. That was deemed necessary by our founding fathers because, primarily, it needed to be exempt from being affected by any state's laws, prejudices, or politics.
To quote part Article I, Section 8 of the U.S. Constitution:
"The Congress shall have the power... To exercise exclusive legislation in all cases whatsoever, over such District (not exceeding ten miles square) as may, by cession of particular states, and the acceptance of Congress, become the seat of the government of the United States, and to exercise like authority over all places purchased by the consent of the legislature of the state in which the same shall be, for the erection of forts, magazines, arsenals, dockyards, and other needful buildings"
http://www.law.cornell.edu/constitut....html#section1