  We calculate in the framework of two Higgs doublet models the differential
decay rate for inclusive $\bar B\to\tau\,\bar\nu\,X$ transitions to order
$1/m_b^2$ in the heavy quark expansion, for both polarized and unpolarized tau
leptons. In contrast to the situation in the standard model, we find sizeable
$1/m_b^2$ corrections. A systematic heavy quark expansion significantly reduces
the theoretical uncertainties in the calculation compared to the existing free
quark decay model results. From the experimental measurement of the branching
ratio, we derive the bound $\tan\beta < 0.51\, m_{H^\pm}\,[{\rm GeV}]$. We
point out that the tau polarization is potentially a more sensitive probe of
multi scalar models than the branching ratio itself.
