  In this paper we consider a possibility to construct dual formulation of
gravity where the main dynamical field is the Lorentz connection
\omega_\mu^{ab} and not that of tetrad e_\mu^a or metric g_\mu\nu. Our approach
is based on the usual dualization procedure which uses first order parent
Lagrangians but in (Anti) de Sitter space and not in the flat Minkowski one. It
turns out that in d=3 dimensions such dual formulation is related with the so
called exotic parity-violating interactions for massless spin-2 particles.
