  We review the parameter regions allowed by measurements of
$\mathcal{R}(D^{(*)})$ and by a theoretical limit on ${\cal
B}(B_{c}\to\tau\nu)$ in terms of generic scalar and pseudoscalar new physics
couplings, $g_s$ and $g_p$. We then use these regions as constraints to predict
the ranges for additional observables in $b\to c\tau\nu$ including the
differential decay distributions $d\Gamma/dq^{2}$; the ratios
$\mathcal{R}(J/\psi)$ and $\mathcal{R}(\Lambda_{c})$; and the tau-lepton
polarisation in $B\to D^{(\star)}\tau\nu$, with emphasis on the CP violating
normal polarisation. Finally we map the allowed regions in $g_s$ and $g_p$ into
the parameters of four versions of the Yukawa couplings of the general 2HDM-III
model. We find that the model is still viable but could be ruled out by a
confirmation of a large $\mathcal{R}(J/\psi)$.
