  In light of recent remarkable progress in Higgs search at the LHC, we study
the rare decay process $h \to Z\gamma$ and show its correlation with the decay
$h \to \gamma\gamma$ in low energy SUSY models such as CMSSM, MSSM, NMSSM and
nMSSM. Under various experimental constraints, we scan the parameter space of
each model, and present in the allowed parameter space the SUSY predictions on
the $Z\gamma$ and $\gamma\gamma$ signal rates in the Higgs production at the
LHC and future e+e- linear colliders. We have following observations: (i)
Compared with the SM prediction, the $Z\gamma$ and $\gamma\gamma$ signal rates
in the CMSSM are both slightly suppressed; (ii) In the MSSM, both the $Z\gamma$
and $\gamma\gamma$ rates can be either enhanced or suppressed, and in optimal
case, the enhancement factors can reach 1.2 and 2 respectively; (iii) In the
NMSSM, the $Z\gamma$ and $\gamma\gamma$ signal rates normalized by their SM
predictions are strongly correlated, and vary from 0.2 to 2; (iv) In the nMSSM,
the $Z\gamma$ and $\gamma\gamma$ rates are greatly reduced. Since the
correlation behavior between the Z\gamma signal and the \gamma\gamma signal is
so model-dependent, it may be used to distinguish the models in future
experiments.
