Context: .At least a fraction of the atomic hydrogen in spiral galaxies is suspected to be the result of molecular hydrogen which has been dissociated by radiation from massive stars. Aims: .In this paper, we extend our earlier set of data from a small region of the Western spiral arm of M 81 with CO observations in order to study the interplay between the radiation field and the molecular and atomic hydrogen. Methods: .We report CO(1-0) observations with the Nobeyama 45 m dish and the Owens Valley interferometer array of selected regions in the Western spiral arm of M 81. Results: .From our Nobeyama data, we detect CO(1-0) emission at several locations, coinciding spatially with HI features near a far-UV source. The levels and widths of the detected CO profiles are consistent with the CO(1-0) emission that can be expected from several large photo-dissociation regions with typical sizes of some 50 × 150 pc located within our telescope beam. We do not detect emission at other pointings, even though several of those are near far-UV sources and accompanied by bright HI. This non-detection is likely a consequence of the marginal area filling factor of photo-dissociation regions in our observations. We detect no emission in our Owens Valley data, consistent with the low intensity of the CO emission detected in that field by the Nobeyama dish. Conclusions: .We explain the lack of CO(1-0) emission at positions farther from far-UV sources as a consequence of insufficient heating and excitation of the molecular gas at these positions, rather than as an absence of molecular hydrogen.