The dissociation process following the Cl K-shell excitation to σ* resonances is studied by high resolution spectroscopy of resonant elastic and inelastic x-ray scattering on CH3Cl, CH2Cl2, CHCl3, and CCl4 molecules. Calculations employing the transition potential and Delta-Kohn-Sham DFT approach are in good agreement with the measured total fluorescence yield and show the presence of a second quasidegenerate group of states with σ* character above the lowest σ* unoccupied molecular orbital for molecules with more than one Cl atom. A bandwidth narrowing and a nonlinear dispersion behavior is extracted from the Kα spectral maps for both σ* resonances. The fitted data indicate that the widths of the Franck-Condon distributions for the first and second σ* resonances are comparable for all the molecules under study. In addition, an asymmetric broadening of the emission peaks is observed for resonant elastic x-ray scattering with zero detuning on both σ* resonances. This is attributed to the fast dissociation, transferring about 0.15 of the scattering probability into higher vibrational modes.