We have searched for CP violation in the decays D0→KS0P0 where P0 denotes a neutral pseudo-scalar meson which is either a π0, η, or η′ using KEKB asymmetric-energy e+e− collision data corresponding to an integrated luminosity of 791 fb−1 collected with the Belle detector. No evidence of significant CP violation is observed. We report the most precise CP asymmetry measurement in the decay D0→KS0π0 to date: ACPD0→KS0π0=(−0.28±0.19±0.10). We also report the first measurements of CP asymmetries in the decays D0→KS0η and D0→KS0η′: ACPD0→KS0η=(+0.54±0.51±0.16) and ACPD0→KS0η′=(+0.98±0.67±0.14), respectively.