We have investigated the ground-state properties of polycrystalline CeCoAsO by means of magnetization, specific heat, and solid-state NMR. Susceptibility and specific-heat measurements suggest a ferromagnetic order at about, T C = 75 K. No further transitions are found down to 0.5 K. At 6.5 K a complex Schottky type of anomaly shows up in the specific-heat results. The interplay between Ce 4f and Co 3d magnetism being responsible for that anomaly is discussed. Furthermore 75 As-NMR investigations have been performed to probe the magnetism on a microscopic scale. As-NMR spectra are analyzed in terms of first and second-order quadrupolar interaction. The anisotropic shift component K ab and K c could be derived from the 75 As powder spectra. Towards lower temperature a strong shift anisotropy was found. Nonetheless K iso tracks the bulk susceptibility down to T = 50 K very well. Furthermore the presence of weak correlations among the Ce ions in the ferromagnetic state is discussed. The observed increase in C / T towards lower temperatures supports this interpretation.