  (Abridged) We compared the quantified morphological properties of 37
intermediate redshift MgII absorption selected galaxies to the properties of
the absorbing halo gas, observed in the spectra of background quasars. The
galaxy morphologies were measured using GIM2D modeling of Hubble Space
Telescope WFPC-2 images and the absorbing gas properties were obtained from
HIRES/Keck and UVES/VLT quasar spectra. We found a 3.1 sigma correlation
between galaxy morphological asymmetries normalized by the quasar-galaxy
projected separations, A/D, and the MgII rest-frame equivalent widths.
Saturation effects cause increased scatter in the relationship with increasing
W_r(2796). We defined a subsample for which the fraction of saturated pixels in
the absorption profiles is f_sat<0.5. The correlation strengthened to 3.3
sigma. We also find a paucity of small morphological asymmetries for galaxies
selected by MgII absorption as compared to those of the general population of
field galaxies, as measured in the Medium Deep Survey. The K-S probability that
the two samples are drawn from the same galaxy population is ruled out at a
99.8% confidence level. The A/D-W_r(2796) correlation suggests a connection
between the processes that perturb galaxies and the quantity of gas in their
halos, normalized by the impact parameter. Since the perturbations are minor,
it is clear that dramatic processes or events are not required for a galaxy to
have an extended halo; the galaxies appear "normal". We suggest that common,
more mild processes that populate halos with gas, such as satellite galaxy
merging, accretion of the local cosmic web, and longer-range galaxy-galaxy
interactions, consequently also induce the observed minor perturbations in the
galaxies.
