Limits on the lepton-flavor-violating reactions ${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$+Z\ensuremath{\rightarrow}${e}^{\mathrm{\ensuremath{-}}}$+Z and ${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$+Z\ensuremath{\rightarrow}${e}^{+}$+(Z-2), muon-electron and muon-positron conversion, have been obtained from a search performed at TRIUMF using a time-projection chamber. Upper limits (90% C.L.) for the branching ratios compared to ordinary muon capture for a titanium target are R---(Ti)=\ensuremath{\Gamma}(${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$Ti\ensuremath{\rightarrow}${\mathit{e}}^{\mathrm{\ensuremath{-}}}$Ti)/\ensuremath{\Gamma}(${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$Ti capture)4.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ and ${\mathit{R}}_{+}$(Ti)=\ensuremath{\Gamma}(${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$Ti\ensuremath{\rightarrow}${\mathit{e}}^{+}$Ca*)/\ensuremath{\Gamma}(${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$Ti capture).1.7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ A smaller data set obtained using a lead target yielded ${R}_{\mathrm{\ensuremath{-}}}$(Pb)4.9\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$. The implications of these results for extensions of the standard model which allow lepton-flavor violation are discussed.