  The excitation function for the $pd\rightarrow$ $d p \pi^{0}$ reaction has
been measured by WASA-at-COSY experiment with the aim of searching for
$^{3}\hspace{-0.03cm}\mbox{He}$-$\eta$ mesic nuclei. The measurement in the
vicinity of $\eta$ meson production was performed using a ramped proton beam.
The data analysis and interpretation was carried out with the assumption that
the $\eta$-mesic Helium decays via the formation of an intermediate
N$^{*}$(1535) resonance. No direct signal of the $\eta$-mesic nucleus is
observed in the excitation function. We determine a new improved upper limit
for the total cross section for the bound state production and decay in the
$pd\rightarrow$ $(^{3}\hspace{-0.03cm}\mbox{He}$-$\eta)_{bound} \rightarrow$ $d
p \pi^{0}$ process. It varies between 13 nb to 24 nb for the bound state with
width in the range $\Gamma \in (5,50)$ MeV.
