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) over bar (0) 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(0)pi(0) decay: A(CP)(D-0 -> K-S(0)pi(0)) = [-0.21 +/- 0.16(stat) +/- 0.07(syst)]%.