  We study the properties of a bosonization procedure based on Clifford algebra
valued degrees of freedom, valid for spaces of any dimension. We present its
interpretation in terms of fermions in presence of $\mathbb{Z}_2$ gauge fields
satisfying a modified Gauss' law, resembling Chern-Simons-like theories. Our
bosonization prescription involves constraints, which are interpreted as a
flatness condition for the gauge field. Solution of the constraints is
presented for toroidal geometries of dimension two. Duality between our model
and $(d-1)$-form $\mathbb{Z}_2$ gauge theory is derived, which elucidates the
relation between the approach taken here with another bosonization map proposed
recently.
