  The anomalies in the measurements of $R_D$ and $R_{D^*}$ continue to provide
motivation for physics beyond the Standard Model. In this work, we assume the
new physics Wilson coefficients to be complex and find their values by doing a
global fit to the present $b\rightarrow c\tau\bar{\nu}$ data. We find that the
number of allowed solutions depend on the choice of the upper limit on
$Br(B_c\rightarrow \tau\bar{\nu})$. We find that the forward-backward
asymmetries in $B\rightarrow (D, D^*)\tau\bar{\nu}$ decays have the capability
to distinguish between different solutions. Further we calculate the maximum
values of CP violating triple product asymmetries in $B\to D^*\tau\bar{\nu}$
decay allowed the current data. We observe that only one of the three CP
asymmetries can be enhanced up to a maximum value of $\sim 2-3\%$ whereas the
other asymmetries remain smaller.
