  We report a measurement of the time-dependent CP-asymmetry parameters $\cal
S$ and $\cal C$ in color-suppressed $B^0 \to D^{(*)0} h^0$ decays, where $h^0$
is a $\pi^0$, $\eta$, or $\omega$ meson, and the $D^0$ decays to one of the CP
eigenstates $K^+K^-$, $K_S\pi^0$, or $K_S\omega$. The data sample consists of
$383\times 10^{6}$ $\Upsilon(4S)\to B\bar{B}$ decays collected with the BABAR
detector at the PEP-II asymmetric-energy $B$-factory at SLAC. The results are
${\cal S}= -0.56 \pm 0.23 \pm 0.05$ and ${\cal C}= -0.23\pm 0.16\pm 0.04$,
where the first error is statistical and the second is systematic.
