We perform the first three-dimensional measurement of the amplitudes of B→ψ(2S)K* and B→χc1K* decays and update our previous measurement for B→J/ψK*. We use a data sample collected with the BABAR detector at the PEP-II storage ring, corresponding to 232×106 BB̄ pairs. The longitudinal polarization of decays involving a JPC=1++ χc1 meson is found to be larger than that with a 1 - J/ψ or ψ(2S) meson. No direct CP-violating charge asymmetry is observed. © 2007 The American Physical Society.