  A search for the dimuon decay of the Standard Model Higgs boson is performed
using the Monte Carlo simulated events to mimic data corresponding to an
integrated luminosity of 5.6 ab$^{-1}$ collected with the Circular
Electron-Positron Collider detector in $e^{+}e^{-}$ collisions at
$\sqrt{s}=240$ GeV. The paper studies $e^{+}e^{-}\to ZH,\,Z\to
q\bar{q},\,H\to\mu^{+}\mu^{-}$ process, and the expected significance
considering only the data statistical uncertainty over the background-only
hypothesis for a Higgs boson with a mass of 125 GeV is found to be 6.1$\sigma$,
corresponding to the precision of 19%. The systematic impacts from the
background Monte Carlo statistical fluctuations are estimated to be negligible.
The dependence of the measurement accuracy on the muon momentum resolution of
the CEPC detector has been investigated. It is found that the muon momentum
resolution has to be better than 204 MeV to discover the $H\to\mu\mu$ process
at the nominal integrated luminosity. And if the resolution is 100% worse than
the designed parameter, the integrated luminosity is needed to be greater than
7.2 ab$^{-1}$ to reach 5$\sigma$ significance.
