The diatomic molecule CP- (X (1) Sigma(+)) is currently experimentally unknown in contrast with its neutral precursor CP (X (2) Sigma(+)) for which the first measurements were performed some 60 years ago. Multireference single and double configuration interaction calculations including a correction for higher-order excitations, employing the augmented correlation-consistent polarized-valence quadruple-zeta basis (aug-cc-pVQZ) were performed on the anionic system CP- (X (1) Sigma(+)) and a variety of properties were examined. Among these we can cite: spectroscopic constants tau(e), omega(e), omega(e)x(e)/y(e), B-e, alpha(e); vibrational and vibrational excitation energies; rotational transitions for several (j', j'') sets and vibrational quantum numbers; selected one-electron properties such as mu(e), Q, q, etc; vibrational and rovibrational dipole moments; line strengths (Einstein A transition coefficients), transition wavenumbers and integrated absorption intensities for several R-branch (Delta J = +1) rotational lines of selected vibrational bands; pure vibrational and rovibrational lifetimes for several vibrational quantum numbers. An instructive comparison has been made with the counterparts of these properties computed for the neutral CP (X (2) Sigma(+)) diatomic molecule.