The dynamics of the C(P-3)+OH(X-2 Pi) -> CO(a(3)Pi)+H(S-2) on its second excited potential energy surface, 1(4)A '', have been investigated in detail by means of an accurate quantum mechanical (QM) time-dependent wave packet (TDWP) approach. Reaction probabilities for values of the total angular momentum J up to 50 are calculated and integral cross sections for a collision energy range which extends up to 0.1 eV are shown. The comparison with quasi-classical trajectory (QCT) and statistical methods reveals the important role played by the double well structure existing in the potential energy surface. The TDWP differential cross sections exhibit a forward-backward symmetry which could be interpreted as indicative of a complex-forming mechanism governing the dynamics of the process. The QM statistical method employed in this study, however, is not capable to reproduce the main features of the possible insertion nature in the reactive collision. The ability to stop individual trajectories selectively at specific locations inside the potential energy surface makes the QCT version of the statistical approach a better option to understand the overall dynamics of the process.