Muon spin relaxation experiments have been performed on DyVO4 and TbVO4, both of which exhibit a cooperative Jahn-Teller transition. The data demonstrate that the nature of the magnetic ion, whether Kramers or non-Kramers, has a decisive effect on the nature of the observed spin relaxation. We interpret this result in terms of the difference in the relaxation induced by the spin-phonon interaction in the two systems.