In order to explain the observed anomalies in the measurements of $R_{D^{\left(\ast \right)}}$ $$ {R}_{D^{\left(\ast \right)}} $$ and R J/ψ , a variety of new-physics (NP) models that contribute to $b\to c{\tau }^{-}\overline{\nu }$ $$ b\to c{\tau}^{-}\overline{\nu} $$ have been proposed. In this paper, we show how CP-violating observables can be used to distinguish these NP models. Because ${\overrightarrow{p}}_{\tau }$ $$ {\overrightarrow{p}}_{\tau } $$ cannot be measured (the decay products of the τ include the undetected ν τ ), obtaining the angular distribution of ${\overline{B}}^0\to D^{\ast +}{\tau }^{-}{\overline{\nu }}_{\tau }$ $$ {\overline{B}}^0\to {D}^{\ast +}{\tau}^{-}{\overline{\nu}}_{\tau } $$ is problematic. Instead, we focus here on ${\overline{B}}^0\to D^{\ast +}\left(\to D^0{\pi }^{+}\right){\mu }^{-}{\overline{\nu }}_{\mu }$ $$ {\overline{B}}^0\to {D}^{\ast +}\left(\to {D}^0{\pi}^{+}\right){\mu}^{-}{\overline{\nu}}_{\mu } $$ . This process may also receive contributions from the same NP, and LHCb intends to measure the CP-violating angular asymmetries in this decay. There are two classes of NP models that contribute to $b\to c{\mu }^{-}{\overline{\nu }}_{{}_{\mu }}$ $$ b\to c{\mu}^{-}{\overline{\nu}}_{{}_{\mu }} $$ . These involve (i) a W ′ (two types) or (ii) a leptoquark (LQ) (six types). The most popular NP models predict no CP-violating effects, so the measurement of nonzero CP-violating asymmetries would rule them out. Furthermore these measurements allow one to distinguish the W ′ and LQ models, and to differentiate among several LQ models.