  In this paper a topological theory of gravity is studied on a four-manifold
using the formalism of Capovilla {\sl et al}. We show that it is fact
equivalent to Anselmi and Fre's topological gravity using the topological
symmetries. Using this formalism gives us a new way to study topological
gravity and the intersection theory of gravitational instantons if the (3+1)
decomposition with respect to local coordinates is performed.
