  In order to explain the observed anomalies in the measurements of
$R_{D^{(*)}}$ and $R_{J/\psi}$, a variety of new-physics (NP) models that
contribute to $b\to c\tau^-{\bar\nu}$ have been proposed. In this paper, we
show how CP-violating observables can be used to distinguish these NP models.
Because ${\vec p}_\tau$ cannot be measured (the decay products of the $\tau$
include the undetected $\nu_\tau$), obtaining the angular distribution of
${\bar B}^0\to D^{*+}\tau^{-}{\bar\nu}_\tau$ is problematic. Instead, we focus
here on ${\bar B}^0\to D^{*+}(\to D^0 \pi^+)\mu^- {\bar\nu}_\mu$. 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 $b\to c\mu^-{\bar\nu}_\mu$. 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
symmetries would rule them out. Furthermore these measurements allow one to
distinguish the $W'$ and LQ models, and to differentiate among several LQ
models.
