We obtain the physical state condition of the bosonized chiral Schwinger model by using BRS symmetry in the presence of the Wess-Zumino term. And the one parameter class of the nominimal anomalies and effective actions are derived by Fujikawa``s path-integral method using the one parameter family of the Euclidean regularization operator. We show that the regularization ambiguity is related to the choice of the nonhermitian chiral operator in calculation of the nonvanishing Jacobian.