Symmetry-resolved excitation spectra have been measured for the Renner-Teller pair states A(1) and B(1) split from the core-excited C 1s(-1)2 pi(u) state in CO(2). A vibrational progression with the spacings of approximately 145 meV is found in both the A(1) and B(1) spectra at different energies and assigned to the symmetric stretching mode caused in the B(1) linear state, with the help of ab initio calculations. Appearance of the vibrations in the A(1) spectrum is interpreted as due to non-adiabatic coupling between the A(1) and B(1) states via the bending motion.