  We clarify the role played by the Immirzi parameter in classical gravity
coupled to fermions. Considering the general non-minimal coupling, we show
that, although the torsion depends explicitly on the Immirzi parameter, in a
suitable parametrization the effective action obtained by integrating out the
spin-connection is independent of it. Thus the Immirzi parameter is not
detectable in classical theory even after coupling of fermions.
