The results of numerical calculations of the energies of Auger transitions, as well as the angular distribution (α₂) and spin polarization (β₂) anisotropy parameters, are presented for transitions in a photoexcited Kr* atom with two open shells. Matrix elements are calculated by the multiconfigurational Fock-Dirac relativistic method using an intermediate type of coupling. The wavefunctions of the initial and final states of the Auger transition are calculated with allowance for relaxation effects. The one-electron wavefunction of the continuous spectrum for an Auger electron is obtained using the single-configuration Fock-Dirac method. The results are compared with experiment and a new experiment is proposed for identifying the Auger state not only from the energy, but also from the total angular momentum of the Auger state.