  We report measurements related to hadronic $B$ decays to final states that
contain charm mesons. The analyses are performed on a $62.8~\mathrm{fb}^{-1}$
data set collected by the Belle II experiment at a center-of-mass energy
corresponding to the mass of the $\Upsilon(4S)$ resonance. The measurements
reported are for the decay modes $B^-\to D^0 h^-$, $B^{-}\to D^{*0}h^-$,
$\bar{B}^{0}\to D^{+} h^{-}$ and $\bar{B}^{0}\to D^{*+} h^{-}$, where $h=\pi$
or $K$. These modes are either signal or control channels for measurements
related to the unitarity triangle angle $\gamma$ in direct or time-dependent
$CP$-violation measurements. The reported observables are the ratios between
the $B\to D^{(*)}K$ and $B\to D^{(*)}\pi$ decay rates, which are found to be in
agreement with previous measurements.
