Can torsion play a role in angular momentum conservation law?
  In Einstein-Cartan theory, by the use of the general Noether theorem, the general covariant angular-momentum conservation law is obtained with the respect to the local Lorentz transformations. The corresponding conservative Noether current is interpreted as the angular momentum tensor of the gravity-matter system including the spin density. It is pointed out that, assuming the tetrad transformation given by eq. (15), torsion tensor can not play a role in the conservation law of angular momentum. 
Yishi Duan, Ying Jiang