Ab initiocalculations, which describe the topography of the potential energy surface of OH(A2Σ+) + CO(X1Σ+) and its interaction with the lowest lying surfaces, OH(X2Π) + CO(X1Σ+), have been used to produce analytical functions for studying the mechanism of electronic quenching with classical mechanics. We distinguish four separate regions on the potential energy surface where quenching occurs, according to the orientation of CO with respect to OH. With the assumption that trapped trajectories lead to quenching with probability equal to one, the contribution of each region to the total quenching cross sections is estimated. The calculated total cross sections are in good agreement with the experimental values. The anisotropy of the potential function justifies the decrease of the quenching cross sections with increase of the initial rotational level of OH. Because of the complex formation the cross sections are also decreased by increasing the collision temperature.