  The consequences of CP and CPT invariance for production and subsequent decay
of Dirac and Majorana fermions in polarized fermion--antifermion annihilation
are analytically studied. We derive general symmetry relations for the
production spin density matrix and for the three--particle decay matrices and
obtain constraints for the polarization and the spin--spin correlations of
Dirac and Majorana fermions. We prove that only for Majorana fermions the
energy and opening angle distribution factorizes exactly into contributions
from production and decay if CP is conserved.
