  The Higgs-boson decay h -> gamma l+ l- for various lepton states l = (e, mu,
tau) is analyzed. The differential decay width and forward-backward asymmetry
are calculated as functions of the dilepton invariant mass in a model where the
Higgs boson interacts with leptons and quarks via a mixture of scalar and
pseudoscalar couplings. These couplings are partly constrained from data on the
decays to leptons, h -> l+ l-, and quarks h -> q \bar{q} (where q = (c, b)),
while the Higgs couplings to the top quark are chosen from the two-photon and
two-gluon decay rates. Nonzero values of the forward-backward asymmetry will
manifest effects of new physics in the Higgs sector. The decay width and
asymmetry integrated over the dilepton invariant mass are also presented.
