  We analyzed the nonleptonic decays $B/B_s\to \psi(2S) V $ with $V=(\rho,
\omega, K^{*}, \phi)$ by employing the perturbative QCD (PQCD) factorization
approach. Here the branching ratios, the $CP$ asymmetries and the complete set
of polarization observables are investigated systematically. Besides the
traditional contributions from the factorizable and nonfactorizable diagrams at
the leading order, the next-to-leading order (NLO) vertex corrections could
also provide considerable contributions. The PQCD predictions for the branching
ratios of the $B_{(s)}\to \psi(2S)K^{*}, \psi(2S) \phi$ decays are consistent
with the measured values within errors. As for $B\to \psi(2S) \rho, \psi(2S)
\omega$ decays, the branching ratios can reach the order of $10^{-5}$ and could
be measured in the LHCb and Belle-II experiments. The numerical results show
that the direct $CP$ asymmetries of the considered decays are very small. Thus
the observation of any large direct $CP$ asymmetry for these decays will be a
signal for new physics. The mixing induced $CP$ asymmetries in the neutral
modes are very close to $\sin 2\beta_{(s)}$, which suggests that these channels
can give a cross-check on the measurement of the Cabbibo-Kobayashi-Maskawa
(CKM) angle $\beta$ and $\beta_s$. We found that the longitudinal polarization
fractions $f_0$ are suppressed to $\sim 50\%$ due to the large nonfactorizable
contributions. The magnitudes and phases of the two transverse amplitudes
$\mathcal {A}_{\parallel}$ and $\mathcal {A}_{\perp}$ are roughly equal, which
is an indication for the approximate light quark helicity conservation in these
decays. The overall polarization observables of $B\to \psi(2S) K^{*0}$ and
$B_s\to \psi(2S) \phi$ channels are also in good agreement with the
experimental measurements as reported by LHCb and BaBar. Other results can also
be tested by the LHCb and Belle-II experiments.
