  A study of semi-inclusive deep inelastic scattering off transversely
polarized $^3$He is presented. The formal expressions of the Collins and Sivers
contributions to the azimuthal single spin asymmetry for the production of
leading pions are derived, in impulse approximation, and estimated in the
kinematics of forth-coming experiments at JLab. The AV18 interaction has been
used for a realistic description of the nuclear dynamics; the nucleon structure
has been described by proper parameterizations of data or suitable model
calculations. The initial transverse momentum of the struck quark has been
properly included in the calculation. The crucial issue of extracting the
neutron information from $^3$He data, planned to shed some light on the
puzzling experimental scenario arisen from recent measurements for the proton
and the deuteron, is thoroughly discussed. It is found that a model independent
procedure, widely used in inclusive deep inelastic scattering to take into
account the momentum and energy distributions of the bound nucleons in $^3$He,
can be applied also in the kinematics of the planned JLab experiments, although
fragmentation functions, not only parton distributions, are involved. The
possible role played by final state interactions in the process under
investigation is addressed.
