We report a search for CP violation in the decay τ⁻ → π⁻ K_S⁰ (0π⁰)ν_τ using a data set of 437×106 τ-lepton pairs, corresponding to an integrated luminosity of 476 fb⁻¹, collected with the BABAR detector at the PEP-II asymmetric-energy e⁺e⁻ storage rings. The CP-violating decay-rate asymmetry is determined to be (-0.36 ± 0.23 ± 0.11)% approximately 2.8 standard deviations from the standard model prediction of (0.36 ± 0.01)%.