We present a study of the decay B-→D(CP)0K- and its charge conjugate, where D(CP)0 is reconstructed in CP-even, CP-odd, and non-CP flavor eigenstates, based on a sample of 232×106 Υ(4S)→BB̄ decays collected with the BABAR detector at the PEP-II e+e- storage ring. We measure the partial-rate charge asymmetries ACP± and the ratios RCP± of the B→D0K decay branching fractions as measured in CP± and non-CP D0 decays: ACP+=0.35±0.13(stat)±0.04(syst), ACP-=-0.06±0. 13(stat)±0.04(syst), RCP+=0.90±0.12(stat)±0.04(syst), and RCP-=0.86±0.10(stat)±0.05(syst). © 2006 The American Physical Society.