The tau -> mu nu nu branching ratio has been measured using data collected from 1990 to 1995 by the OPAL detector at the LEP collider. The resulting value of B(tau -> mu nu nu) = 0.1734 +- 0.0009(stat) +- 0.0006(syst) has been used in conjunction with other OPAL measurements to test lepton universality, yielding the coupling constant ratios gmu/ge=1.0005+-0.0044 and gt/ge=1.0031+-0.0048, in good agreement with the Standard Model prediction of unity. A value for the Michel parameter eta = 0.004 +- 0.037 has also been determined and used to find a limit for the mass of the charged Higgs boson mH+- > 1.25 tan beta, in the Minimal Supersymmetric Standard Model.