  We have searched for $D^0 - \bar{D}^0$ mixing in $D^{*+} \to \pi^+ D^0$
decays with $D^0 \to K^{(*)} e \nu$ in a sample of $e^+ e^- \to {c\bar c}$
events produced near 10.58 GeV. The charge of the slow pion from charged $D^*$
decay tags the charm flavor at production, and it is required to be consistent
with the flavor of a fully reconstructed second charm decay in the same event.
We observe 3 mixed candidates compared to 2.85 background events expected from
simulation. We ascribe a 50% systematic uncertainty to this expected background
rate. We find a central value for the mixing rate of $0.4 \times 10^{-4}$.
Using a frequentist method, we set corresponding 68% and 90% confidence
intervals at $(-5.6, 7.4) \times 10^{-4}$ and $(-13, 12) \times 10^{-4}$,
respectively.
