Search for CP violation in $e^{+}{e}^{-}\to \psi (3770)\to D^0{\bar{D}}^0$ via $D->K_S^0{\pi }^0$

Utilizing data sample of electron-positron collisions recorded with the BESIII detector at the center of mass energy of 3.773 GeV, corresponding to an integrated luminosity of 20.28 fb${}^{-1}$, we report the first search for the CP forbidden process $e^{+}{e}^{-}\to \psi (3773)\to D^0{\bar{D}}^0\to (K_S^0{\pi }^0)(K_S^0{\pi }^0)$. No significant signal is observed. We set the upper limit on the observed cross section to be 7.37 fb, and the upper limit on the joint branching fraction of the C-odd correlated neutral $D$ pair $\mathcal{B}[(D^0{\bar{D}}^0{)}_{\text{C-odd}}\to (K_S^0{\pi }^0)(K_S^0{\pi }^0)]<2.04\times {10}^{-6}$ at the 90% confidence level.