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We study the properties of the spin-dependent one-body density in momentum space for odd-A polarized deformed nuclei within the mean field approximation. We derive analytic expressions connecting intrinsic and laboratory momentum distributions. The latter are related to observable transition densities in p-space that can be proved in one nucleon knockout reactions from polarized targets. It is shown that most of the information contained in the intrinsic spin-dependent momentum distribution is lost when the nucleus is not polarized. Results are presented and discussed for two prolate nuclei, 21Ne and 25Mg, and for one oblate nucleus, 37Ar. The effects of deformation are highlighted by comparison to the case of odd-A nuclei in the spherical model.Copyright 1995, 1999 Academic Press, Inc.