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The differential rate of the decay of the Higgs boson ($h$) to a pair of$\tau $ leptons with their subsequent decay in the $\tau^-\to \pi^- \nu_\tau$and $\tau^+\to \pi^+{\bar \nu}_\tau$ channels is studied. The Yukawainteraction between the Higgs boson and the $\tau$ leptons is assumed toinclude scalar ($S$) and pseudoscalar ($PS$) couplings. Angular distributionsof the pions in the $h\to\tau^- \tau^+\to\pi^-\nu_{\tau}\,\pi^+{\bar \nu}_\tau$decay are considered. For real values of the $S$ and $PS$ couplings, this decayis known to be a source of information on $\mathcal{CP}$ violation in the $h\tau \tau $ interaction. In the present paper, the main attention is paid to apossible non-Hermiticity of this interaction. Influence of non-Hermiticity onthe distribution of the angle between planes of the $ \tau^- \to\pi^-\nu_{\tau}$ and $\tau^+ \to \pi^+ {\bar \nu}_{\tau}$ decays, anddistribution of the polar angle of one of the pions are analyzed. Asymmetriessensitive to parameters of $\mathcal{CP}$ violation and non-Hermiticity of $h\tau \tau$ interaction are proposed.

Decay of the Higgs boson $h\to\tau^- \tau^+\to\pi^-\nu_{\tau}\,\pi^+{\bar \nu}_\tau$ for a non-Hermitian Yukawa interaction