  We present complementary data on 5 intermediate redshift (0.44 < z < 0.66)
MgII absorbing galaxies, combining high spatial resolution imaging from HST,
high--resolution QSO spectroscopy from Keck/HIRES, and galaxy kinematics from
intermediate resolution spectroscopy using Keck/LRIS. These data allow a direct
comparison of the kinematics of gas at large galactocentric impact parameters
with the galaxy kinematics obtained from the faint galaxy spectroscopy. All 5
galaxies appear to be relatively normal spirals, with measured rotation curves
yielding circular velocities in the range 100 < v_c < 260 km/s. We find that in
4 of the 5 cases examined, the velocities of all of the Mg II absorption
components lie entirely to one side of the galaxy systemic redshift. These
observations are consistent with rotation being dominant for the absorbing gas
kinematics; however, the total range of velocities observed is inconsistent
with simple disk rotation in every case. Simple kinematic models that
simultaneously explain both the systemic offset of the absorbing material
relative to the galaxy redshifts, and the total velocity width spanned by the
absorption, require either extremely thick rotating gas layers, rotation
velocities that vary with height above the extrapolation of the galactic plane,
or both. In any case, our small sample suggests that rotating ``halo'' gas is a
common feature of intermediate redshift spiral galaxies, and that the kinematic
signature of rotation dominates over radial infall or outflow even for gas well
away from the galactic plane. We discuss possible explanations for this
behavior, and compare our observations to possible local analogs.
