  We explore the nonuniversal interaction effects in terms of the precision
variables epsilons with the recent LEP data reported by the Electroweak Working
Group. The epsilon variables with the nonuniversal interactions are calculated
and constrained by the experimental ellipses in the $\epsilon_1$--$\epsilon_b$,
$\epsilon_2$--$\epsilon_b$, and $\epsilon_3$--$\epsilon_b$ planes. We find that
the new data enables us to make a stringent test on the correction to $Z \to b
\bar{b}$ vertex. The $\epsilon_b$ variable is sensitive to the $Z b \bar b$
couplings and thus plays a major role to give constraints on the nonuniversal
interaction effects. Upon imposing the new data on $\epsilon_b$, we have the
allowed range of the model parameter $\kappa_L = 0.0063 \pm 0.0030$ at
1-$\sigma$ level with $m_t = 175$ GeV. Along with the minimal contact term, we
predict the new physics scale $\Lambda \sim$ 1.6 TeV. By combining the
experimental results from all planes we obtain the allowed range of $\kappa_L$
: $0.003 < \kappa_L < 0.010$ at 95 % C.L..
