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The ratio of branching fractions $R(D^{*}) = \mathcal{B}(\overline{B}\rightarrow D^{*} \tau^{-} \overline{\nu}_{\tau})$/$\mathcal{B} (\overline{B}\rightarrow D^{*} \ell^{-} \overline{\nu}_{\ell})$, where $\ell$ is an electronor muon, is measured using a Belle~II data sample with an integrated luminosityof $189~\mathrm{fb}^{-1}$ at the SuperKEKB asymmetric-energy $e^{+} e^{-}$collider. Data is collected at the $\Upsilon(\mathrm{4S})$ resonance, and one$B$ meson in the $\Upsilon(\mathrm{4S})\rightarrow B\overline{B}$ decay isfully reconstructed in hadronic decay modes. The accompanying signal $B$ mesonis reconstructed as $\overline{B}\rightarrow D^{*}\tau^{-}\overline{\nu}_{\tau}$ using leptonic $\tau$ decays. The normalizationdecay, $\overline{B}\rightarrow D^{*} \ell^{-} \overline{\nu}_{\ell}$, where$\ell$ is an electron or muon, produces the same observable final stateparticles. The ratio of branching fractions is extracted in a simultaneous fitto two signal-discriminating variables in both channels and yields $R(D^{*}) =0.262~_{-0.039}^{+0.041}(\mathrm{stat})~_{-0.032}^{+0.035}(\mathrm{syst})$.This result is consistent with the current world average and with standardmodel predictions.

A test of lepton flavor universality with a measurement of $R(D^{*})$ using hadronic $B$ tagging at the Belle II experiment