the $(d-{\rm critical\ dimensions}+1)$ non-proportional correction of the BRST (super-)current in the left hand side is generated from the Liouville correction of the ghost number (super-)current in the right hand side. If we expect the general validity of the relation  in our construction, the BRST supercurrent in the $N=2$ super-Liouville theory will not have $d-1$ non-proportional correction. Actually, we can check  from the explicit form . In the BRST current algebra like  in the $N=0$ and $N=1$ case \[,,\], we can also observe that the anomalous terms in the algebra arise from the above mentioned non-trivial correction of the BRST and ghost number (super-)currents. In the case of $N=2$, therefore, we may expect the anomaly free property of the operator algebra.

It is also useful to see how the critical string can be considered as a subcritical string in dimension 1 plus the Liouville superfield, in fact in this situation, $\kappa=0$ and all the operators of the effective theory coincide with the ones of the critical string, since in this case there is no restriction for the possible values of $d$.

Conclusion
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We computed the BRST and the ghost number anomalies in the $N=2$ supergravity in the superconformal gauge, 