We present a preliminary study of $B-\to DCP0\pi -$ and $B-\to DCP0K-$ decays, with the $DCP0$ reconstructed in the CP-odd eigenstates $Ks\pi 0$, $Ks\omega$, in the CP-even eigenstates $K+K-$, $\pi +\pi -$, and in the (non-CP) flavor eigenstate $K\mp \pi \pm$. Using a sample of about 382 million Y(4S) decays into BBbar pairs, collected with the BABAR detector operating at the PEP-II asymmetric-energy B Factory at SLAC, we measure the ratios of the branching fractions R_CP+- and the direct CP asymmetries A_CP+-. The results are: R_CP- = 0.81 \pm 0.10 (stat) \pm 0.05 (syst) R_CP+ = 1.07 \pm 0.10 (stat) \pm 0.04 (syst) A_CP- = -0.19 \pm 0.12 (stat) \pm 0.02 (syst) A_CP+ = 0.35 \pm 0.09 (stat) \pm 0.05 (syst)