Search for the charmonium weak decay $J\mathrm{/}\psi \to {\bar{D}}^0{\bar{K}}^{\ast 0}+\mathrm{c}\mathrm{.}\mathrm{c}\mathrm{.}$

Based on a sample of $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected at the center-of-mass energy $\sqrt{s}$ = 3.0969 GeV with the BESIII detector, we search for the charmonium rare weak decay $J\mathrm{/}\psi \to {\bar{D}}^0{\bar{K}}^{\ast 0}+\mathrm{c}\mathrm{.}\mathrm{c}\mathrm{.}$. No significant signal is observed, and the upper limit on its decay branching fraction at the 90% confidence level is set as $1.4\times {10}^{-7}$, improving the sensitivity of the previous best limit by an order of magnitude.