  We report a study of B -> D*K decays with D* decaying to D pi0 or D gamma,
using 383 * 10**6 B Bbar pairs collected at the Upsilon(4S) resonance with the
BaBar detector at the SLAC PEP-II B-Factory. The D meson decays under study
include a non-CP mode (Kpi), CP-even modes (K+K-, pi^+pi^-) and CP-odd modes
(KS pi0, KS phi, KS omega). We measure ratios (R*_{CP+-}) of branching
fractions of decays to CP eigenmode states and to flavor-specific states as
well as CP asymmetries (A*_{CP+-}). These measurements are sensitive to the
unitarity triangle angle gamma. We obtain A*_{CP+} = -0.11 pm 0.09 pm 0.01,
R*_{CP+} = ~1.31 pm 0.13 pm 0.04, and A*_{CP-} = 0.06 pm 0.10 pm 0.02, R*_{CP-}
= ~1.10 pm 0.12 pm 0.04, where the first error is statistical and the second
error is systematic. Translating our results into an alternative
parametrization, widely used for related measurements, we obtain x*_{+}=0.11 pm
0.06 pm 0.02 and x*_{-} = 0.00 pm 0.06 pm 0.02. No significant CP-violating
charge asymmetry is found in either the flavor-specific mode D -> K pi or in B
-> D* pi decays.
