  We have analyzed the supersymmetric tri-lepton signals for sparticle searches
at the Tevatron in the minimal supersymmetric standard model with general CP
phases without generational mixing. The CP phases may affect very strongly the
chargino and neutralino mass spectrums and
$\sigma(p\bar{p}\to\tilde{\chi}^-_1\tilde{\chi}^0_2)$ as well as ${\cal
B}(\tilde{\chi}^-_1\to\tilde{\chi}^0_1\ell^-\nu)$ and ${\cal
B}(\tilde{\chi}^0_2\to\tilde{\chi}^0_1\ell^+\ell^-)$. Even under the stringent
constraints from the electron electric dipole moment the CP phases can lead to
a minimum of the tri-lepton event rate for their non-trivial values.
