Redefining B-twisted topological sigma models

A recently proposed variation on the usual procedure to perform the topological B-twist in rigid $N=2$ models is applied to the case of the $\sigma$ model on a K\"ahler manifold. This leads to an alternative description of Witten's topological $\sigma$ model, which allows for a proper BRST interpretation and ghost number assignement. We also show that the auxiliary fields, which are responsible for the off shell closure of the $N=2$ algebra, play an important role in our construction.