Motivated by the high muon momentum resolution and identification efficiency achievable with the ATLAS detector, currently being installed at CERN, we explore the observability of the supersymmetric h/A/H decays to two muons. The high experimental resolution in this decay mode compensates to some extent for the suppression of the branching ratio, with respect to the h/A/H → τ τ decays. The search is performed in a wide Higgs mass range, starting from 110 GeV/c2. In the case of gg → bb(h/H/A) production mode, the additional b-jets produced in association with the h/H/A bosons are used to suppress the background. Using fully simulated signal and background event samples, we study the performance of the reconstruction algorithms relevant to the analysis, such as the muon reconstruction, b-tagging and the measurement of the missing energy. The influence of the detector misalignment on the reconstruction performance is also taken into consideration. Emphasis is given on the optimization of the event selection procedure and the corresponding selection criteria, taking into account the different background composition depending on the mass range in which the Higgs search is performed.