  We discuss on the possible existence of a supersymmetric invariance in purely
fermionic planar systems and its relation to the fermion-boson mapping in
three-dimensional quantum field theory. We consider, as a very simple example,
the bosonization of free massive fermions and show that, under certain
conditions on the masses, this model displays a supersymmetric-like invariance
in the low energy regime. We construct the purely fermionic expression for the
supercurrent and the non-linear supersymmetry transformation laws. We argue
that the supersymmetry is absent in the limit of massless fermions where the
bosonized theory is non-local.
