  Using the grassman-number-integral representation of the vacuum overlap
formula, it is shown that the symmetry of the auxiliary quantum fermion system
in the overlap formalism induces exact chiral symmetry of the action of the
type given by Luscher under the chiral transformation $\delta \psi_n =
\gamma_5(1-a D)\psi_n$ and $ \delta \bar \psi_n = \bar \psi_n \gamma_5$. With
this relation, we consider the connection between the covariant form of the
anomaly discussed in the context of the overlap formula and the axial anomaly
associated to the exact chiral symmetry in the action formalism. The covariant
gauge current in the overlap formalism is translated to the action formalism
and its explicit expression is obtained.
