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The CMS Collaboration has reported a possible lepton flavor violating (LFV) signal h→μτ. Whereas this does not happen in the standard model (SM), we point out that new physics responsible for this type of decay would, in general, also produce charge-parity (CP) violation in h→ττ. We estimate the size of this effect in a model independent manner and find that a large asymmetry, of order 25%, is allowed by current constraints.