  In our previous study, we calculated the transition from factors of
$J/\psi\to D^{(*)}_{(s)}$ using the QCD sum rules. Based on the factorization
approximation, the obtained form factors can be applied to evaluate the weak
non-leptonic decay rates of $J/\psi\to D^{(*)}_{(s)}+M$, where $M$ stands for a
light pseudoscalar or vector meson. We predict that the branching ratio for
inclusive non-leptonic two-body weak decays of $J/\psi$ which are realized via
the spectator mechanism, can be as large as $1.3 \times 10^{-8}$, in
particular, the branching ratio of $J/\psi\to D^{*\pm}_s+\rho^\mp$ can reach
$5.3 \times 10^{-9}$. Such values will be marginally accessed by the ability of
BESIII which will begin running very soon.
