  We study the Lorentz and CPT violating effects on the branching ratio BR, the
CPT violating asymmetry A_{CPT} and the ratio of the decay width, including
only the Lorentz violating effects, to the one obtained in the standard model,
for the flavor dependent part of the lepton flavor conserving Z\to l^+ l^-
(l=e,\mu,\tau) decay. The inclusion of the Lorentz and CPT violating effects to
the standard model contribution is too small to be detected, since the
corresponding coefficients are highly suppressed at the low energy scale.
