CP violation in hto ττ and LFV hto μτ

The CMS collaboration has reported a possible lepton flavour violating (LFV) signal $h\to\mu\tau$. 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 $h\to \tau\tau$. 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.