  The rate of the nuclear reaction $^3He+\mu^- \to ^3H+\gamma+\nu_{\mu}$ has
been calculated using both the elementary particle model (EPM) approach and the
impulse approximation (IA) approach. Using the EPM approach, the exclusive
statistical radiative muon capture (RMC) rate for photon energy greater than 57
MeV is found to be $0.245 s^{-1}$ and the ordinary muon capture (OMC) rate to
be $1503 s^{-1}$. The IA calculation exhibits a slight dependence on the type
of trinucleon wave functions used. The difference between the IA and EPM
calculation is larger for RMC than for OMC. To resolve the difference between
the two approaches a more detailed investigation including meson exchange
corrections will be required.
