Asymmetry parameter values have been determined from the C+ and O+ signals in the time of flight mass spectra of CO excited and/or ionized with monochromatic synchrotron radiation around the C K and 0 K ionization edges using a rotatable time of flight mass spectrometer. Asymmetry parameter values of about -0.8 were obtained from the C+ and O+ ions at the positions of both the C1s(-1)2pi* and O1s(-1)2pi* resonances below the core edges. Positive values of about 0.5 were obtained at the positions of the sigma shape resonances above the C and 0 K edges. The results are consistent with previous assignments of the symmetries of the final state orbitals for the pre-edge resonances and the symmetries of the outgoing channels which exhibit shape resonances above the C K and 0 K ionization edges. The results are also consistent with the recently reported symmetry resolved photoionization spectra of CO. Above the ionization edges, the experimental data shows good agreement with the molecular asymmetry parameter values calculated by the relaxed-core Hartree-Fock method. Effects of the relatively intense shake-up transitions accompanying C1s ionization on the asymmetry parameter values are considered.