  The possible transverse polarization of the $\tau$-lepton, which is $T$-odd
and can be used to measure CP-violation, is estimated precisely in the
radiative decay mode $B_c \to \tau \bar \nu_\tau \gamma$ with possible
parameters for the multi Higgs doublet model and the R-parity violating
supersymmetric model. We find that the up-bound of the transverse polarization
with possible parameters in the models is at very different levels i.e. it can
be $\leq 15\sim 23%$ for the former but $\leq 0.1 %$ for the latter, and it is
accessible experimentally soon.
