  Limits on $\nu_\mu (\overline{\nu}_\mu) \to \nu_e (\overline{\nu}_e)$
oscillations based on a statistical separation of $\nu_e N$ charged current
interactions in the CCFR detector at Fermilab are presented. $\nu_e$
interactions are identified by the difference in the longitudinal shower energy
deposition pattern of $\nu_e N \rightarrow eX$ versus $\nu_\mu N \to \nu_\mu X$
interactions. Neutrino energies range from 30 to 600 GeV with a mean of 140
GeV, and $\nu_\mu$ flight lengths vary from 0.9 km to 1.4 km. The lowest 90%
confidence upper limit in $sin^2 2\alpha$ of $1.1 \times 10^{-3}$ is obtained
at $\Delta m^2 \sim 300 eV^2$. For $sin^2 2\alpha = 1$, $\Delta m^2 > 1.6 eV^2$
is excluded, and for $\Delta m^2 \gg 1000 eV^2$, $sin^2 2\alpha > 1.8 \times
10^{-3}$ is excluded. This result is the most stringent limit to date for
$\Delta m^2 > 25 eV^2$ and it excludes the high $\Delta m^2$ oscillation region
favoured by the LSND experiment. The $\nu_\mu$-to-$\nu_e$ cross-section ratio
was measured as a test of $\nu_\mu (\bar\nu_\mu) \leftrightarrow \nu_e
(\bar\nu_e)$ universality to be $1.026 \pm 0.055$.
