  We consider an arbitrary U(1) charged matter non-minimally coupled to the
self-dual field in $d=2+1$. The coupling includes a linear and a rather general
quadratic term in the self-dual field. By using both a Lagragian gauge
embedding and a master action approaches we derive the dual Maxwell
Chern-Simons type model and show the classical equivalence between the two
theories. At quantum level the master action approach in general requires the
addition of an awkward extra term to the Maxwell Chern-Simons type theory. Only
in the case of a linear coupling in the self-dual field the extra term can be
dropped and we are able to establish the quantum equivalence of gauge invariant
correlation functions in both theories.
