  A Monte Carlo study of possible background processes in a search for $\tau
\to \mu \gamma$ decay has been performed for conditions of the Super $c-\tau$
factory (CTF) (at a center-of-mass energy 3.686 GeV, 3.77 GeV and 4.17 GeV).
The background from $\tau^{+}\tau^{-}$ events has been analysed. Selection
criteria for background suppression are suggested and necessary requirements on
the detector characteristics have been found. The CTF can successfully compete
with the Super B-factory in a search for $\tau \to \mu \gamma$ decay.
