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Possibility of using the polarized nucleus target for testing thenon-standard properties of fermionic dark matter is considered. It is assumedthat the incoming dark matter scatters on the polarized nuclei in the presenceof vector, axial, scalar and tensor interactions. The scalar and tensorcouplings are assumed to be complex numbers. Various types of measurementsettings are tested depending on the assumptions regarding dark matterpolarization and measurement of the recoil nucleus spin. In particular weaddress the question of finding and distinguishing effects of theoreticallypossible scenarios in which mixed triple products among various polarizationvectors, the momenta of incoming dark matter and of recoil nucleus appear inthe cross section. Their presence would indicate the possibility of timereversal symmetry violation in the polarized dark matter-nucleus scattering.Our considerations are model-independent and carried out in thenon-relativistic dark matter and recoiled nucleus limit.

Polarized target as a tool for probing the non-standard properties of dark matter