  A search for the rare decays of $J/\psi \to D_s^-\rho^+ + c.c.$ and $J/\psi
\to \overline{D}{}^0\overline{K}{}^{\ast0} + c.c.$ is performed with a data
sample of 225.3 million $J/\psi$ events collected with the BESIII detector. No
evident signal is observed. Upper limits on the branching fractions are
determined to be $\mathcal{B}(J/\psi \to D_s^-\rho^+ + c.c.) < 1.3 \times
10^{-5}$ and $\mathcal{B}(J/\psi \to \overline{D}{}^0\overline{K}{}^{\ast0} +
c.c.) < 2.5 \times 10^{-6}$ at the $90\%$ confidence level.
