We report measurements of CP violation parameters in B-0 -> K-0 pi(0) decays based on a data sample of 657 X 10(6)B (B) over bar pairs collected with the Belle detector at the KEKB e(+)e(-) asymmetric-energy collider. We use B-0 -> K-S(0)pi(0) decays for both mixing-induced and direct CP violating asymmetry measurements and B-0 -> K-L(0)pi(0) decays for the direct CP violation measurement. The CP violation parameters obtained are sin2 phi(eff)(1) - +0.67 +/- 0.31(stat) +/- 0.08(syst) and A(K0 pi 0) - +0.14 +/- 0.13(stat) +/- 0.06(syst). The branching fraction of B-0 -> K-0 pi(0) decay is measured to be B(B-0 -> K-0 pi(0)) - (8.7 +/- 0.5(stat) +/- 0.6(syst)) X 10(-6). The observed A(K0 pi 0) value differs by 1.9 standard deviations from the value expected from an isospin sum rule.