This report presents the results of an experiment aimed at observation of the muon catalyzed $^3!He;d$ fusion reaction $^3!He + mu;dto^3!He;mu;dto^4!He(3.66MeV)+p(14.64MeV)+mu$ 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 $N_{bg}=2.2pm 0.3$ events. This gives an upper limit for the probability of the fusion decay of the $^3!He;mu;d$ molecule $P_{F}(^3!He;mu;d)leq 1.1cdot 10^{-7}$ 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 $q_{1S}=0.80(3)$.
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