Search for CP violation in $e^{+}e^{-} \to ψ(3770) \to D^{0}\bar{D}^{0}$ via $D -> K^{0}_{S} π^{0}$

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 $e^+e^- \to ψ(3773) \to D^0\bar{D}^0 \to (K^0_Sπ^0)(K^0_Sπ^0)$. 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 $\mathcal{B}[(D^{0} \bar{D}^{0})_{\text{C-odd}} \to (K^{0}_{S} π^{0})(K^{0}_{S} π^{0})] < 2.04 \times 10^{-6}$ at the 90% confidence level.