We present a measurement of the ratio Rμ=Bτ−→μ−ν ̄μντ/Bτ−→e−ν ̄eντ of branching fractions B of the τ lepton decaying to muons or electrons using data collected with the Belle II detector at the SuperKEKB e+e− collider. The sample has an integrated luminosity of 362 ± 2 fb−1 at a centre-of-mass energy of 10.58 GeV. Using an optimised event selection, a binned maximum likelihood fit is performed using the momentum spectra of the electron and muon candidates. The result, Rμ = 0.9675 ± 0.0007 ± 0.0036, where the first uncertainty is statistical and the second is systematic, is the most precise to date. It provides a stringent test of the light-lepton universality, translating to a ratio of the couplings of the muon and electron to the W boson in τ decays of 0.9974 ± 0.0019, in agreement with the standard model expectation of unity.
