We compute the supersymmetry (SUSY) effective Hamiltonian that describes the vertical bar Delta S vertical bar=1 semileptonic decays of tau leptons. We provide analytical expressions for supersymmetric contribution to tau -> u (s) over bar nu(tau) transition in mass insertion approximation. We show that SUSY contributions may enhance the CP asymmetry of tau -> K pi nu(tau) decays by several orders of magnitude with respect to the standard model expectations. However, the resulting asymmetry is still well below the current experimental limits obtained by CLEO Collaborations. We emphasize that measuring CP rate asymmetry in this decay larger than 10(-6) would be a clear evidence of physics beyond the supersymmetric extensions of the standard model.