The C(P-3) + OH(X (2)Pi) -> CO(X (1)Sigma(g) (+)) + H(S-2) reaction has been investigated by ab initio electronic structure calculations of the X(2)A ' state based on the multireference (MR) internally contracted single and double configuration interaction (SDCI) method plus Davidson correction (+ Q) using Dunning aug-cc-pVQZ basis sets. In particular, the multireference space is taken to be a complete active space (CAS). Improvement over previously proposed potential energy surfaces for HCO/COH is obtained in the sense that present surface describes also the potential part where the CO interatomic distance is large. A large number of geometries (around 2000) have been calculated and analytically fitted using the reproducing kernel Hilbert space (RKHS) method of Ho and Rabitz both for the two-body and three-body terms following the many-body decomposition of the total electronic energies. Results show that the global reaction is highly exothermic (similar to 6.4 eV) and barrierless (relative to the reactant channel), while five potential barriers are located on this surface. The three minima and five saddle points observed are characterized and found to be in good agreement with previous work. The three minima correspond to the formation of HCO and COH complexes and to the CO + H products, with the COH complex being a metastable minimum relative to the product channel. The five saddle points correspond to potential barriers for both the dissociation/formation of HCO and COH into/from CO + H, to barriers for the isomerization of HCO into COH and to barriers for the inversion of HCO and COH through their respective linear configuration.