  Based on a path integral prescription for anomaly calculation, we analyze an
effective theory of the two-dimensional $N=2$ supergravity, i.e., $N=2$
super-Liouville theory. We calculate the anomalies associated with the BRST
supercurrent and the ghost number supercurrent. From those expressions of
anomalies, we construct covariant BRST and ghost number supercurrents in the
effective theory. We then show that the (super-)coordinate BRST current algebra
forms a superfield extension of the topological conformal algebra for an {\it
arbitrary\/} type of conformal matter or, in terms of the string theory, for an
arbitrary number of space-time dimensions. This fact is very contrast with
$N=0$ and $N=1$ (super-)Liouville theory, where the topological algebra singles
out a particular value of dimensions. Our observation suggests a topological
nature of the two-dimensional $N=2$ supergravity as a quantum theory.
