  Supergravity in 2+1 dimensions has a set of first class constraints that
result in two Bosonic and one Fermionic gauge invariances. When one uses
Faddeev-Popov quantization, these gauge invariances result in four Fermionic
scalar ghosts and two Bosonic Majorana spinor ghosts. The BRST invariance of
the effective Lagrangian is found. As an example of a radiative correction, we
compute the phase of the one-loop effective action in the presence of a
background spin connection, and show that it vanishes. This indicates that
unlike a spinor coupled to a gauge field in 2 + 1 dimensions, there is no
dynamical generation of a topological mass in this model. An additional example
of how a BRST invariant invariant effective action can arise in a gauge theory
is provided in an appendix where the BRST invariant effective action for the
classical Palatini action in 1+1 dimensions is examined.
