  We present a study of the $\tau$ polarization in charged-current quasielastic
(anti)neutrino-nucleus scattering. The spectral function formalism is used to
compute the differential cross section and the polarization components for
several kinematical setups, relevant for neutrino-oscillation experiments. The
effects of the nuclear corrections in these observables are investigated by
comparing the results obtained using two different realistic spectral
functions, with those deduced from the relativistic global Fermi gas model,
where only statistical correlations are accounted for. We show that the
spectral functions, although they play an important role when predicting the
differential cross sections, produce much less visible effects on the
polarization components of the outgoing $\tau$.
