Co-doped ZnO films are epitaxially grown on sapphire by reactive magnetron sputtering. The preparation conditions such as temperature and the composition of the sputtering gas are systematically varied. For optimized growth conditions virtually all Co dopant atoms are located on substitutional Zn lattice sites as revealed by X-ray linear dichroism (XLD). The material behaves as a Brillouin-like paramagnet with S = 3/2 and L = 1 as revealed by integral and element specific magnetometry. Reducing the oxygen content during preparation leads to the onset of phase separation as revealed by X-ray diffraction, and more clearly by a strong reduction of the XLD signal. Such samples behave like a blocked superparamagnetic ensemble. In the entire range of preparation conditions no signs of intrinsic ferromagnetism are found.