We consider a supersymmetric theory in an arbitrary 2+1 dimensional curved background containing a U(1) and a Dirac spin-1/2 fields. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields (gauge and matter) enter as parts of the connection, that transforms in the adjoint representation of the gauge group. The system is off-shell invariant under supersymmetry. Although the supersymmetry is realized, there is no spin-3/2 gravitino, it is not therefore standard supergravity. The fields do not necessarily form supersymmetric doublets of equal mass, and moreover, fermions may acquire mass through the coupling with geometry, while the bosons -the U(1) field and the spin connection-remain massless. Finally, we present the generalization to four dimensions.