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Utilizing data samples 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− → ψ(3773) → D0D0 → (K0Sπ0)(K0Sπ0). 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 B[(D0D0)C-odd → (K0Sπ0)(K0Sπ0)] < 2.04 × 10−6 at the 90% confidence level.