The branching fraction ratio R (D*) ≡B (B̄ 0→D*+τ-ν̄ τ)/B (B̄ 0→D*+μ-ν̄ μ) is measured using a sample of proton-proton collision data corresponding to 3.0 fb-1 of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode τ-→μ-ν̄μντ. 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 B̄0 decays gives R (D*) =0.336 ±0.027 (stat )±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.