The respiratory system would have no blood to "ship" oxygen to, plus, with the circulatory system failing, the human would die as a whole, since the muscles and organs will end up failing without blood coursing through them to energize them.
Essentially what I'm saying is that it wouldn't matter what happens to the respiratory system because everything else would fail if the circulatory system fails. Meaning that the respiratory system will shut down as well.
I know that this isn't the best answer, but I hope it helps!