  We report on an improved study of $\bar{B}^0 \to D^{(*)0} \bar{K}^{(*)0}$
decays, based on $274 \times 10^6$ $B{\bar B}$ events collected with the Belle
detector at KEKB. The following branching fractions have been measured: ${\cal
B}(\bar{B}^0 \to D^0 \bar{K}^0) = (3.72 \pm 0.65 \pm 0.37) \times 10^{-5}$ and
${\cal B}(\bar{B}^0 \to D^0 \bar{K}^{*0}) = (3.08 \pm 0.56 \pm 0.31) \times
10^{-5}$. We also obtain evidence with $3.2\sigma$ significance for $\bar{B}^0
\to D^{*0} \bar{K}^0$ with ${\cal B}(\bar{B}^0 \to D^{*0} \bar{K}^0) =
(3.2^{+1.2}_{-1.1} \pm 0.4) \times 10^{-5}$. No significant signal has been
found for the $\bar{B}^0 \to D^{*0} \bar{K}^{*0}$ and $\bar{B}^0 \to
\bar{D}^{(*)0} \bar{K}^{*0}$ decay modes, and upper limits at 90% CL are
presented.
