  Present experimental datas have shown a 3.8$\sigma$ level discrepancy with
the standard model in $\overline{B}\to D^{(*)}\tau\bar{\nu}_{\tau}$. Some new
physics models have been considered to explain this discrepancy possibly with
new source of the CP violation. In this paper, we construct CP violating
observables by using multi-pion decays in $B\to D\tau\nu_{\tau}$, and estimate
sensitivity of these observables to generic CP violating operators. We also
discuss possibilities of CP violation in leptoquark models and in 2HDM of
type-III.
