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 $\rho \text{−}\omega$ 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 $D^0\to K^0{\overline{K}}^{*0}$, ${\overline{K}}^0{K}^{*0}$, $D^{+}\to {\pi }^{+}{\rho }^0$, and $D_s^{+}\to K^{+}\omega$, $K^{+}\varphi$ decays are found to be of $\mathcal{O}({10}^{-3})$, which can be observed at the LHCb and future Belle II experiment. We also predict the $CP$ asymmetry observables of some neutral $D$ meson decays.

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