  The Circular Electron Positron Collider (CEPC) is a future Higgs factory
proposed by the Chinese high energy physics community. It will operate at a
center-of-mass energy of 240-250 GeV. The CEPC will accumulate an integrated
luminosity of 5 ab$^{\rm{-1}}$ in ten years' operation, producing one million
Higgs bosons via the Higgsstrahlung and vector boson fusion processes. This
sample allows a percent or even sub-percent level determination of the Higgs
boson couplings. With GEANT4-based full simulation and dedicated fast
simulation tool, we evaluated the statistical precisions of the Higgstrahlung
cross section $\sigma_{ZH}$ and the Higgs mass $m_{H}$ measurement at the CEPC
in the $Z\rightarrow\mu^+\mu^-$ channel. The statistical precision of
$\sigma_{ZH}$ ($m_{H}$) measurement could reach 0.97\% (6.9 MeV) in the
model-independent analysis which uses only the information of Z boson decay.
For the standard model Higgs boson, the $m_{H}$ precision could be improved to
5.4 MeV by including the information of Higgs decays. Impact of the TPC size to
these measurements is investigated. In addition, we studied the prospect of
measuring the Higgs boson decaying into invisible final states at the CEPC.
With the standard model $ZH$ production rate, the upper limit of ${\cal
B}(H\rightarrow \rm{inv.})$ could reach 1.2\% at 95\% confidence level.
