By means of capture γ-ray spectroscopy with a polarized target and/or a polarized neutron beam, spin values could be assigned uniquely to 13 levels in 56Mn, six of which are new: J = 3 for the levels 341, 486, 2089 and 2255 keV and J = 2 for the 2321 and 2441 keV levels. For 16 primary transitions the relative contribution of the reaction channel with spin 3 could be derived. Further the sign of the magnetic hyperfine field at the Mn nuclei was established as being negative in MnSb.