Observations of the nucleus of M82 obtained with the 12-m Kitt Peak antenna show that the CO J = 1 to 2 peak temperature structure possesses a dual-core morphology similar to that found at J = 1 to 0. The results indicate that the predominant regime of low opacity gas is located to the north of the star-burst zone, suggesting that material to the south of the core is dissociated by an intense local radiation field and that material to the north is accreted from a low-metallicity low-density H-I halo, ultimately to coalesce with a central accretion disk. The possible contribution of an optically thin component of emission is considered.