We present the first complete (CO)-C-12 J = 3- 2 map of M81, observed as part of the Nearby Galaxies Legacy Survey being carried out at the James Clerk Maxwell Telescope. We detect nine regions of significant CO emission located at different positions within the spiral arms, and confirm that the global CO emission in the galaxy is low. We combine these data with a new Ha map obtained using the Isaac Newton Telescope and archival HI, 24 mu m, and FUV images to uncover a correlation between the molecular gas and star forming regions in M81. For the nine regions detected in CO J = 3- 2, we combine our CO J = 3- 2 data with existing CO J = 1-0 data to calculate line ratios. We find that the ratio J = (3-2)/(1-0) is in agreement with the range of typical values found in the literature (0.2-0.8). Making reasonable assumptions, this allows us to constrain the hydrogen density to the range (10(3)-10(4)) cm(-3). We also estimated the amount of hydrogen produced in photo-dissociation regions near the locations where CO J = 3- 2 was detected.