The upper critical field of most polycrystalline NbN thin films is anisotropic, with the perpendicular critical field Hc2(1) larger than the parallel critical field Hc2(11). We have measured the angular dependence Hc2(e) for samples with both a columnar and non-columnar microstructure In both cases we find a rounded maximum near Hc2(1). The shape of HC2 (e), combined with the known microstructure of the films and the linear temperature dependence of Hc2 for. both field orientations leads us to conclude that the mechanism responsible for this anisotropy is an anisotropic conductivity in the film, probably due to differences in the grain boundary resistance in the plane of the film and normal to the film. In contrast, a single crystal film shows only surface superconductivity.