The semileptonic $CP$ asymmetry in ${B}^{0}$-${\overline{B}}^{0}$ mixing, ${a}_{\text{sl}}^{d}$, is measured in proton-proton collision data, corresponding to an integrated luminosity of $3.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, recorded by the LHCb experiment. Semileptonic ${B}^{0}$ decays are reconstructed in the inclusive final states ${D}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}$ and ${D}^{*\ensuremath{-}}{\ensuremath{\mu}}^{+}$, where the ${D}^{\ensuremath{-}}$ meson decays into the ${K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ final state and the ${D}^{*\ensuremath{-}}$ meson into the ${\overline{D}}^{0}(\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}){\ensuremath{\pi}}^{\ensuremath{-}}$ final state. The asymmetry between the numbers of ${D}^{(*)\ensuremath{-}}{\ensuremath{\mu}}^{+}$ and ${D}^{(*)+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decays is measured as a function of the decay time of the ${B}^{0}$ mesons. The $CP$ asymmetry is measured to be ${a}_{\text{sl}}^{d}=(\ensuremath{-}0.02\ifmmode\pm\else\textpm\fi{}0.19\ifmmode\pm\else\textpm\fi{}0.30)%$, where the first uncertainty is statistical and the second systematic. This is the most precise measurement of ${a}_{\text{sl}}^{d}$ to date and is consistent with the prediction from the standard model.