CO2+ dissociative recombination has been assumed in the past to proceed overwhelmingly by the channel that produces CO + O. Although the channel that leads to the products C + O2 is energetically possible, the significant rearrangement of bonds that is required has led to the belief that this channel contributes minimally. Seiersen et al. <2003> have recently measured the branching ratio for the latter channel, and they have reported a value of ~9% of the total. We have constructed both low and high solar activity models of the Martian thermosphere, and we have tested the effect of including the C + O2 channel on the production of both thermal and escaping C atoms in the Martian atmosphere. We find that dissociative recombination of CO2+ is by far the dominant source of atomic carbon in both models, and its inclusion leads to larger densities of ambient C. The contribution of the source to the escape flux of C, however, is found to be small, both because the altitude profile of the production rate falls off rapidly near the exobase and because the O2 molecule is probably produced with considerable internal energy. A calculation of the statistical energy partitioning into vibrational and rotational energy of the product O2 molecule and the translational energy of the products of the reaction indicates that the C atom is produced with translational energy exceeding the escape energy only 3.7% of the time. The models predict that photodissociation of CO is the most important source of escaping C, as have other recent investigations. The computed escape fluxes for the minor sources, however, differ considerably from those of previous models. We find that the second most important source of escaping C is electron impact dissociation of CO, followed by dissociative recombination of CO+. The total predicted escape fluxes are comparable to those of previous models at high solar activity and are a factor of 2 larger at low solar activity.