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The ratios of branching fractions $\mathcal{R}({D}^{*})\ensuremath{\equiv}\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{D}^{*}{\ensuremath{\tau}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}})/\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{D}^{*}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})$ and $\mathcal{R}({D}^{0})\ensuremath{\equiv}\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\tau}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}})/\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})$ are measured, assuming isospin symmetry, using a sample of proton-proton collision data corresponding to $3.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$. The measured values are $\mathcal{R}({D}^{*})=0.281\ifmmode\pm\else\textpm\fi{}0.018\ifmmode\pm\else\textpm\fi{}0.024$ and $\mathcal{R}({D}^{0})=0.441\ifmmode\pm\else\textpm\fi{}0.060\ifmmode\pm\else\textpm\fi{}0.066$, where the first uncertainty is statistical and the second is systematic. The correlation between these measurements is $\ensuremath{\rho}=\ensuremath{-}0.43$. The results are consistent with the current average of these quantities and are at a combined 1.9 standard deviations from the predictions based on lepton flavor universality in the standard model.