  We study CP violation in fermion pair decays of neutral boson particles with
spin 0 or 1. We study a new asymmetry to measure CP violation in $\eta, K_L
\rightarrow \mu^+\mu^-$ decays and discuss the possibility of measuring it
experimentally. For the spin-1 particles case, we study CP violation in the
decays of $J/\psi$ to $SU(3)$ octet baryon pairs. We show that these decays can
be used to put stringent constraints on the electric dipole moments of
$\Lambda$, $\Sigma$ and $\Xi$.
