  We perform the first three-dimensional measurement of the amplitudes of $B\to
\psi(2S) K^*$ and $B\to \chi_{c1} K^*$ decays and update our previous
measurement for $B\to J/\psi K^*$. We use a data sample collected with the
BaBar detector at the PEP2 storage ring, corresponding to 232 million $B\bar B$
pairs. The longitudinal polarization of decays involving a $J^{PC}=1^{++}$
$\chi_{c1}$ meson is found to be larger than that with a $1^{--}$ $J/\psi$ or
$\psi(2S)$ meson. No direct {\it CP}-violating charge asymmetry is observed.
