  Motivated by the rapid development of heavy-flavor experiments,
phenomenological studies of nonleptonic $\bar{B}_{d,s} \to D^{*}_{d,s} V$ and
$\bar{B}_{d,s}^* \to D_{d,s} V$~($V=\rho\,,K^*$) decays are performed within
the framework of QCD Factorization. Relative to previous works, the QCD
corrections to the transverse amplitudes are evaluated at next-to-leading
order. The theoretical predictions of the observables are updated. For the
measured $\bar{B}_{d,s} \to D^{*}_{d,s} V$ decays, two tensions between
theoretical results and experimental measurements, {\it i.e.} "$R_{ds}^{V}$
puzzle" and "$D^{*} V$~(or $R_{V/\ell\bar{\nu}_\ell}$) puzzle", are presented
after detailed analyses. For the $\bar{B}_{d,s}^* \to D_{d,s} V$ decays, they
have relatively large branching fractions of the order $\gtrsim{\cal
O}(10^{-9})$ and are in the scope of Belle-II and LHCb experiments. Moreover,
they also provide a way to crosscheck the above-mentioned possible puzzles
through the similar ratios $R_{ds}^{\prime V}$ and
$R_{V/\ell\bar{\nu}_\ell}^{\prime}$. More refined experimental measurements and
theoretical efforts are required to confirm or refute such two anomalies.
