  Precise descriptions are given for the operator product expansion of generic
primary fields as well as the factorization of four point functions as sum over
intermediate states. The conjecture underlying the recent derivation of the
space-time current algebra for string theory on $ADS_3$ by Kutasov and Seiberg
is thereby verified. The roles of microscopic and macroscopic states are
further clarified. The present work provides the conformal field theory
prerequisites for a future study of factorization of amplitudes for string
theory on $ADS_3$ as well as operator product expansion in the corresponding
conformal field theory on the boundary.
