The central arcminute of the Perseus cooling flow galaxy, NGC 1275, has been mapped with the JCMT in 12 CO(2-1) at 21 ′′ resolution, with detections out to at least 36 ′′ (12 kpc). Within the limits of the resolution and coverage, the distribution of gas appears to be roughly E-W, consistent with previous observations of CO, X-ray, Hα, and dust emission. The total detected molecular hydrogen mass is ∼ 1.6 × 10 10 M ⊙ , using a Galactic conversion factor. The inner central rotating disk is apparent in the data, but the overall distribution is not one of rotation. Rather, the line profiles are bluewards asymmetric, consistent with previous observations in HI and [OIII]. We suggest that the blueshift may be due to an acquired mean velocity of ∼ 150 km s −1 imparted by the radio jet in the advancing direction. Within the uncertainties of the analysis, the available radio energy appears to be sufficient, and the interpretation is consistent with that of Bohringer et al. (1993) for displaced X-ray emission.We have also made the first observations of 13 CO(2-1) and 12 CO(3-2) emission from the central 21 ′′ region of NGC 1275 and combined these data with IRAM data supplied by Reuter et al. (1993) to form line ratios over equivalent, well-sampled regions. An LVG radiative transfer analysis indicates that the line ratios are not well reproduced by a single value of kinetic temperature, molecular hydrogen density, and abundance per unit velocity gradient. At least two temperatures are suggested by a simple two-component LVG model, possibly reflecting a temperature gradient in this region.