Possible approaches to experimentally detecting P-parity violation in polarized proton or deuteron interactions with an unpolarized target are discussed. Within the first approach, a polarized proton or deuteron beam is scattered on a thick internal target deployed in one of rings of the NICA collider, and the spin state of the circulating beam is transformed to the mode of precession in the horizontal plane using an RF spin flipper. In this case, parity-violating effects can be probed by measuring the correlation between the interaction cross section and the particle spin direction. In an alternative experimental approach, beam-particle spins are rotated into the horizontal plane using a spin flipper, and then the beam is extracted to a beamline at a definite stage of spin precession. In this experimental scheme, which can be viewed as more traditional, one then collides the extracted beam with a dense external target and compares the measured cross sections for particles with opposite helicities passing through the target.