The ratios Rτ=P ≡ Γðτ → Pντ½γ Þ=ΓðP → μνμ½γ Þ (P ¼ π, K) provide sensitive tests of lepton universality jgτ=gμj ¼ 1 and are a useful tool for new physics searches. The radiative corrections to Rτ=P are computed following a large-NC expansion to deal with hadronic effects: Chiral Perturbation Theory is enlarged by including the lightest multiplets of spin-one heavy states such that the relevant Green functions are well behaved at high energies. We find δRτ=π ¼ ð0.18 0.57Þ% and δRτ=K ¼ ð0.97 0.58Þ%, which imply jgτ=gμjπ ¼ 0.9964 0.0038 and jgτ=gμjK ¼ 0.9857 0.0078, compatible with and at 1.8σ of lepton universality, respectively. We test unitarity and bind nonstandard effective interactions with the τ → Pντ½γ decays.