We suggest measuring the nuclear-spin-dependent P-odd amplitude in the transitions between hyperfine structure sublevels in the ground state of potassium isotopes. Since the main contribution to this amplitude is due to the anapole moment of the nucleus, such measurements of the P-odd spin-dependent effects may provide new information about weak interactions. It is established that the measurement of such effects with a statistical error within 1% can be performed for approximately 1 h.