Limits on Flavor Changing Neutral Currents in ${\mathit{D}}^0$ Meson Decays

Using the CLEO II detector at the Cornell Electron Storage Ring, we have searched for flavor changing neutral currents and lepton family number violations in $D^0$ meson decays. The upper limits on the branching fractions for $D^0\to {\ell }^{+}{\ell }^{-}$ and $D^0\to X^0{\ell }^{+}{\ell }^{-}$ are in the range ${10}^{-5\mathrm{}}$ to ${10}^{-4\mathrm{}}$, where $X^0$ can be a ${\pi }^0$, $K_s^0$, $\eta$, ${\rho }^0$, $\omega$, ${\overline{K}}^{*0\mathrm{}}$, or $\phi$ meson, and the ${\ell }^{+}{\ell }^{-}$ pair can be $e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}$, or $e^{\pm }{\mu }^{\mp }$. Although these limits are above the theoretical predictions, most are new or an order of magnitude lower than previous limits.