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.