  In this article a theoretical model for the $\eta$-mesic
$^{3}\hspace{-0.03cm}\mbox{He}$ non-mesonic decay channels is presented. We
present the resultant relative momentum distribution of bound
$^{3}\hspace{-0.03cm}\mbox{He}$-$\eta$ as well as in-medium branching ratios of
$\eta\rightarrow 2\gamma$ and $\eta\rightarrow 3\pi^0$, which are crucial for
the Monte Carlo simulations of measured processes and thus for the experimental
data interpretation. As an example we also apply the model for the estimation
of the detection efficiency of the WASA-at-COSY detector.
