In order to investigate the ferromagnetism of Co-doped ZnO, we systematically fabricated Zn1−xCoxO (x = 0, 0.05, 0.1, 0.2, 0.4) thin films on (0001) Al2O3 substrates by rf-sputtering and measured their structural, electronic, optical, and magnetic properties. Below 20 mol% of Co, the Co ion could be successfully substituted at Zn site and showed clear paramagnetism in superconducting quantum interference devices (SQUID) and magnetic circular dichroism (MCD)measurements. However, secondary phases, including Co metal clustering, were found in the ZnO matrix at a 40-mol% Co concentration, showing a strong ferromagnetism due to the contributes of microscopic precipitates of Co ions. Consequently, the clear paramagnetic behaviors of all the fabricated ZnCoO thin films in the magneto-optic MCD results revealed that the spin-polarized band structure, an intrinsic property of ferromagnetism diluted ferromagnetic semiconductors (DMSs),could not be induced by the substituted Co ions themselves. Importantly, these results indicate that any intrinsic ferromagnetism in ZnCoO cannot be induced without the contribution of hydrogen.