  To clarify some issues raised by D'Eath's recent proposal for the physical
states of $N=1$ supergravity in four dimensions, we study pure (topological)
$N=2$ supergravity in three dimensions, which is formally very similar, but
much easier to solve. The wave functionals solving the quantum constraints can
be understood in terms of arbitrary functions on the space of moduli and
supermoduli, which is not Hausdorff. We discuss the implications for the wave
functionals and show that these are not amenable to expansions in fermionic
coordinates, but can serve as lowest-order solutions to the quantum constraints
in an expansion in $\hbar$ in more realistic theories.
