The generalized energy corrected sudden model is used to calculate the Q branch of the anisotropic coherent anti-Stokes Raman scattering spectra corresponding to the nu(1) and 2 nu(2) transitions of the Fermi dyad of CO2. The corresponding experimental spectra have been recorded for pressures leading to a consistent overlapping between the rotational components. This leads to a new experimental evaluation of the relaxation time of the second-order tensor associated with the rotational angular momentum. The value is in excellent agreement with that already obtained from the study of the infrared absorption Q branch, the Rayleigh scattering, and the viscomagnetic effect.