The branching fraction ratio $mathcal{R}(D^{*}) equiv mathcal{B}(overline{B}^0 to D^{*+}tau^{-}overline{ u}_{tau})/mathcal{B}(overline{B}^0 to D^{*+}mu^{-}overline{ u}_{mu})$ is measured using a sample of proton-proton collision data corresponding to 3.0invfb of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode $tau^{-} to mu^{-}overline{ u}_{mu} u_{tau}$. The semitauonic decay is sensitive to contributions from non-Standard-Model particles that preferentially couple to the third generation of fermions, in particular Higgs-like charged scalars. A multidimensional fit to kinematic distributions of the candidate $overline{B}^0$ decays gives $mathcal{R}(D^{*}) = 0.336 pm 0.027(stat) pm 0.030 (syst)$. This result, which is the first measurement of this quantity at a hadron collider, is $2.1$ standard deviations larger than the value expected from lepton universality in the Standard Model.