We study possible New Physics (NP) effects in the exclusive decays $\bar{B}^0 \to D^{(\ast)} \tau^- \bar{\nu}_{\tau}$. We extend the Standard Model (SM) by taking into account right-handed vector (axial), left- and right-handed (pseudo)scalar, and tensor current contributions... The $\bar{B}^0 \to D^{(\ast)}$ transition form factors are calculated in the full kinematic $q^2$ range by employing a covariant quark model developed by us. We provide constraints on NP operators based on measurements of the ratios of branching fractions $R(D^{(\ast)}) \equiv \mathcal{B}(\bar{B}^0 \to D^{(\ast)} \tau^- \bar{\nu}_{\tau})/ \mathcal{B}(\bar{B}^0 \to D^{(\ast)} \mu^- \bar{\nu}_{\mu})$ and consider the effects of these operators on physical observables in different NP scenarios. We also derive the four-fold angular distribution for the cascade decay $\bar {B}^0\to D^{\ast\,+}(\to D^0\pi^+)\tau^-\bar\nu_\tau$ which allows one to analyze the polarization of the $D^{\ast}$ meson in the presence of NP effects. We discuss several strategies to distinguish between various NP contributions. (read more)