Observations of a broad area at the core of M82, obtained with spatial resolution 30 arcsec and velocity resolution 15.6 km/sec in the J = 2-1 line of CO using the 12-m NRAO antenna at KPNO, are reported. The data are presented in graphs and contour maps and characterized in detail. It is found that the J = 2-1 map is similar to the J = 1-0 map of Olofsson and Rydbeck (1984), but that the emission maximum is significantly north of the J = 1-0 emission core and the location of the X-ray maximum. It is suggested that the tenuous accreted material responsible for the CO emission north of the core may be unable to survive the more rigorous dissociating radiation field to the south.