  This report presents the results of an experiment aimed at observation of the
muon catalyzed $^3\!He\;d$ fusion reaction $^3\!He +
\mu\;d\to^3\!He\;\mu\;d\to^4\!He(3.66MeV)+p(14.64MeV)+\mu$ which might occur
after a negative muon stop in the $D_2+^3\!He$ gas mixture. The basic element
of the experimental setup is a Time Projection Chamber (TPC) which can detect
the incoming muons and the products of the fusion reaction. The TPC operated
with the $D_2 + ^3\~He (5%)$ gas mixture at $31K$ temperature. About $10^8$
$^3\!He\;\mu\;d$ molecules were produced with only 2 registered candidates for
the muon catalyzed $^3\!He\;d$ fusion with the expected background
$N_{bg}=2.2\pm 0.3$ events. This gives an upper limit for the probability of
the fusion decay of the $^3\!He\;\mu\;d$ molecule $P_{F}(^3\!He\;\mu\;d)\leq
1.1\cdot 10^{-7}$ at 90% C.L. Also presented are the measured formation rate of
the $^3\!He\;\mu\;d$ molecule $\lambda_{d3He}=192(3)\cdot 10^6 s^{-1}$ and the
probability of the fast muon transfer from the excited to the ground state of
the $\mu\;d$ atom $q_{1S}=0.80(3)$.
