We have performed an experiment in which a polarized electron beam ionizes an orbitally oriented and/or spin-polarized valence electron of sodium. The cross section for this reaction is measured for well-resolved vector momenta of the two electrons in the final channel. In order to study the transfer of the initial spin and orbital orientation from the electron-atom system to the final-state correlated electron pair, we develop a tensorial recoupling scheme in which the measured quantities are expressed in terms of independent, irreducible spherical tensor components. By this procedure the cross section is separated into terms characterized by their specific rotational transformation properties, decoupling of geometrical effects due to initial-state preparation from effects associated with details of the scattering dynamics is achieved, and exchange and orbital angular momentum transfer effects are disentangled. For a comparison with experiment we performed numerical ionization-cross section calculations within the distorted wave Born approximation and the dynamically screened three Coulomb waves theory. For some tensorial parameters significant discrepancies between theory and experiment are observed that underline the importance of the state-specific measurements as stringent tests of scattering theories.