The canonical theory of (N = 1) supergravity, with a matrix representa
tion for the gravitino covector-spinor, is applied to the Bianchi clas
s A spatially homogeneous cosmologies. The full Lorentz constraint and
its implications for the wave function of the universe are analyzed i
n detail. We found that in this model no physical states other than th
e trivial ''rest frame'' type occur.