  One of the main channels which allows for a large rate of neutralino dark
matter annihilation in the early Universe is via the pseudoscalar Higgs
A-resonance. In this case, the measured dark matter abundance can be obtained
in the minimal supergravity (mSUGRA) model when tan(beta)\sim 50 and
2m_{\tz_1}\sim m_A. We investigate the reaction pp\to b\phi\to b\mu^+\mu^- +X
(where \phi =A or H) at the CERN LHC where requiring the tag of a single b-jet
allows for amplification of the signal-to-background ratio. The rare but
observable Higgs decay to muon pairs allows for a precise measurement of the
Higgs boson mass and decay width. We evaluate signal and background using
CalcHEP, with muon energy smearing according to the CMS detector. We find that
the Higgs width (\Gamma_A) can typically be determined with the accuracy up to
\sim 8% (\sim 17%) for m_A\sim 400 (600) GeV assuming 10^3 fb^{-1} of
integrated luminosity. Therefore, the pp\to b\phi\to b\mu^+\mu^- +X process
provides a unique possibility for direct \Gamma_A measurement at the LHC. While
the Higgs width is correlated with the parameter \tan\beta for a given value of
m_A, extracting \tan\beta is complicated by an overlap of the A and H peaks,
radiative corrections to the b and \tau Yukawa couplings, and the possibility
that SUSY decay modes of the Higgs may be open. In the case where a dilepton
mass edge from \tz_2\to\ell^+\ell^-\tz_1 is visible, it should be possible to
test the relation that 2m_{\tz_1}\sim m_A.
