Simultaneous theoretical and experimental study of the angular asymmetry parameter β for the O K-shell of CO molecule has been performed. Transitions from the ground vibrational level of the neutral molecule to the vibrational states of the ion with v ′ = 0 , 1 , 2 , were studied in the region of the σ ∗ shape resonance. Calculations in the relaxed core Hartree–Fock approximation with a fractional charge are in a qualitative agreement with the experiment. The theory demonstrates that the dipole amplitudes with different orbital angular momentum l have different behavior with increasing v ′ which explains the observed variation of β .