Torsion in kerr black holes

In General Relativity, we generally assume that the derivative operator is torsion-free, i.e., second covariant derivatives commute on functions.

However, in Kerr black holes, spacetime is dragged (especially in the ergosphere), so it seems that there is torsion in this case.

Geometrically, why there isn't torsion in the Kerr spacetime? What is the geometric interpretation of torsion if Kerr spacetime doesn't have it?