Using synchrotron radiation, very high resolution electron spectra at the 2p --> 6a(1) and 2p --> 3b(2) resonances of H2S have been recorded. Auger transitions from molecular field split S 2p hole states of HS* fragment, created by fast dissociation of the core excited H2S, are found to reveal different partial rates depending on the symmetry of the final state. The experiments have made it possible to determine, for the first time, the molecular field splitting of the core levels in a free radical. The molecular field splitting between the 3 sigma(1/2) and 1 pi(3/2) ("2P(3/2)") levels in the HS* fragment is found to be 90(5) meV, which significantly differs from the molecular field splitting of the "S 2p(3/2)" levels in the H2S molecule. Resonant Auger decay in the molecule before dissociation is also observed.