  We study the functional integrals that appear in a path integral bosonization
procedure for more than two spacetime dimensions. Since they are not in general
exactly solvable, their evaluation by a suitable loop expansion would be a
natural procedure, even if the exact fermionic determinant were known. The
outcome of our study is that we can consistently ignore loop corrections in the
functional integral defining the bosonized action, if the same is done for the
functional integral corresponding to the bosonic representation of the
generating functional. If contributions up to some order $l$ in the number of
loops are included in both integrals, all but the lowest terms cancel out in
the final result for the generating functional.
