The first run of the Belle II experiment collected a 365 $\rm fb^{-1}$ sample of collisions at a centre-of-mass energy corresponding to the $\Upsilon (4S)$ resonance. These data, characterised by low particle multiplicity, well-constrained initial-state kinematics, and excellent lepton identification, provide an ideal environment to study lepton-flavour universality in semileptonic $B$ decays. We present results on the ratios of semitauonic decay rates compared to those to light leptons in both exclusive and inclusive $B$ decay. These include new measurements of the ratios for exclusive $B\to D^{(*)}\ell \nu_{\ell}$ decays $R(D^{(*)})_{\tau/\ell}$ in events tagged by a semileptonic $B$ decay.