Accurate calculations were performed for several doublet and quartet states of CO+ using the multireference configuration interaction method. With a single set of molecular orbitals the accurate transition dipole moments were evaluated. The calculated lifetimes of the vibronic states of the A (2)Pi and B (2)Sigma(+) states were in excellent agreement with the available experimental data. The calculated vibrational spacings and rotational constants up to upsilon = 40 of the X (2)Sigma(+) state were compared with the latest experimental data, and quantitative agreement was attained.