  The differential rate of the decay of the Higgs boson ($h$) to a pair of
$\tau $ leptons with their subsequent decay in the channels $\tau^-\to \pi^-
\nu_\tau$ and $\tau^+\to \pi^+{\bar \nu}_\tau$ is studied. The Yukawa
interaction between the Higgs boson and the $\tau$ leptons is assumed to
include scalar ($S$) and pseudoscalar ($PS$) couplings. Angular distributions
of the pions in the decay $h\to\tau^- \tau^+\to\pi^-\nu_{\tau}\,\pi^+{\bar
\nu}_\tau$ are considered. For real values of the $S$ and $PS$ couplings this
decay is 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
a non-Hermiticity of this interaction. Influence of non-Hermiticity on the
distribution of the angle between planes of the decays $\tau^- \to
\pi^-\nu_{\tau}$ and $\tau^+ \to \pi^+ {\bar \nu}_{\tau}$, and distribution of
the polar angle of one of the pions are analyzed. Asymmetries sensitive to
parameters of $\mathcal{CP}$ violation and non-Hermiticity of $h \tau \tau$
interaction are proposed.
