We search for CP violation in neutral charm meson decays using a data sample with an integrated luminosity of 966 fb^-1 collected with the Belle detector at the KEKB e+e- asymmetric-energy collider. The asymmetry obtained in the rate of D^0 and D^0-bar decays to the pi^0 pi^0 final state, [-0.03+-0.64(stat)+-0.10(syst)]%, is consistent with no CP violation. This constitutes an order of magnitude improvement over the existing result. We also present an updated measurement of the CP asymmetry in the D^0 -> K_S pi^0 decay: A_{CP}(D^0 -> K_S pi^0) = [-0.21+-0.16(stat)+-0.07(syst)]%.