The present theoretical calculations on CP X2Σ+, A2Π, 14Σ+, 14∆, 14Π, 16Π and 16Σ+ electronic states use standard and explicitly correlated coupled cluster approaches, multi-reference configuration interaction (MRCI) techniques in connection with a large panel of basis sets. We also examined core-valence (CV) and scalar relativistic (SR) effects. For the ground electronic state, our calculations reveal that the MRCI+CV+SR method and the coupled cluster technique with perturbative treatment of triple excitations including scalar relativistic effects computed with the Douglas-Kroll approach (RCCSD[T]-DK) in connection with a large basis set lead to an accurate description of CP(X2Σ+). We computed the evolution along the internuclear distance of the diagonal and the off-diagonal spin-orbit integrals between the X2Σ+ and A2Π states. These integrals are then incorporated together with the corresponding potentials into variational treatment of the nuclear motion. We deduced hence the energy positions of the low and high vibronic levels of X2Σ+ and A2Π states. Finally, it is shown the necessity of considering the spin-orbit coupling for accurate prediction of the energy position of these levels.