  The conformal structure of second order in $m$-dimensions together with the
so-called (normal) conformal Cartan connection, is considered as a framework
for gauge theories. The dressing field scheme presented in a previous work
amounts to a decoupling of both the inversion and the Lorentz symmetries such
that the residual gauge symmetry is the Weyl symmetry. On the one hand, it
provides straightforwardly the Riemannian parametrization of the normal
conformal Cartan connection and its curvature. On the other hand, it also
provides the finite transformation laws under the Weyl rescaling of the various
geometric objects involved. Subsequently, the dressing field method is shown to
fit the BRS differential algebra treatment of infinitesimal gauge symmetry. The
dressed ghost field encoding the residual Weyl symmetry is presented. The
related so-called algebraic connection supplies relevant combinations found in
the literature in the algebraic study of the Weyl anomaly.
