The JWs say Nehemiah wrote Nehemiah, but Jewish tradition says Ezra authored/edited Chronicles/Ezra/Nehemiah the last 2 which were originally 1 book until separated by the Greeks.
My source is the NIV study bible.
What souces does the WT have for their information?
Compare the apocryphal ESDRAS to Ezra/Nehemiah and you'll see that Nehemiah returned from Babylon with Zerubbabel, but because of the chronological revisions for the Persian period, this fact had to be suppressed. The apocryphal ESDRAS was meant to both harmonize with the revised chronology while the original EZRA/NEMIAH was suppressed, as well as give clues to the original chronology.