  We study the two-body hadronic $D\to PV$ decays, where $P$ ($V$) denotes a
pseudoscalar (vector) meson, in the factorization-assisted
topological-amplitude approach proposed in our previous work. This approach is
based on the factorization of short-distance and long-distance dynamics into
Wilson coefficients and hadronic matrix elements of four-fermion operators,
respectively, with the latter being parametrized in terms of several
nonperturbative quantities. We further take into account the $\rho$-$\omega$
mixing effect, which improves the global fit to the branching ratios involving
the $\rho^0$ and $\omega$ mesons. Combining short-distance dynamics associated
with penguin operators and the hadronic parameters determined from the global
fit to branching ratios, we predict direct $CP$ asymmetries. In particular, the
direct $CP$ asymmetries in the $D^0\to
K^0\overline{K}^{*0},~\overline{K}^0K^{*0}$, $D^+\to\pi^+\rho^0$, and $D_s^+\to
K^+\omega,~K^+\phi$ decays are found to be of ${\cal O}(10^{-3})$, which can be
observed at the LHCb or future Belle II experiment. We also predict the $CP$
asymmetry observables of some neutral $D$ meson decays.
