Present world averages of $R_D$ and $R_{D^*}$ measurements are in disagreement with their Standard Model (SM) predictions at a level of $\sim 3.1\sigma$. Assuming the new physics Wilson coefficients to be complex, we do a global fit to the present $b\rightarrow c\,\tau\,\bar{\nu}$ data. We find that there are only one/two/three allowed solutions depending upon three choices on upper limits $10\%$/$30\%$/$60\%$ of $Br(B_c\rightarrow \tau\,\bar{\nu})$. Further we calculate the maximum values of CP violating triple product asymmetries in $B\to D^*\tau\bar{\nu}$ decay allowed by the current data. We find that one of the three asymmetries can be enhanced up to only $\sim 2-3\%$ due to presence of the allowed new physics solutions.