  We have studied the tau-lepton polarization in the charged current
$\nu_\tau/\bar\nu_\tau$ induced deep inelastic scattering (DIS) from the free
nucleon as well as off the nuclear targets that are being used in ongoing and
proposed experiments such as IceCube, DUNE, etc. For the free nucleon target,
the differential scattering cross sections are obtained by taking into account
the non-perturbative effect like target mass corrections (TMC) and the
perturbative effect like the evolution of the parton densities at the
next-to-leading order (NLO) in the four flavor $\overline{\textrm{MS}}-$scheme.
In the case of nucleons bound inside a nuclear target, we have incorporated the
nuclear medium effects such as Fermi motion, binding energy and nucleon
correlations, through the use of nucleon spectral function. We shall present
the results for the differential scattering cross sections and the longitudinal
and transverse components of the tau-lepton polarization assuming time reversal
invariance.
