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)]%