  Searches are being carried out at the Large Hadron Collider (LHC) for the
decay of the CP-odd scalar ($A^0$) in Two-Higgs-Doublet Models (2HDMs) with
Natural Flavour Conservation (NFC) in the channel $A^0\to h^0 Z$ (with
$m_{h^0}=125$ GeV and $Z$ on-shell). In the absence of any signal, limits on
the parameter space of $[\tan\beta, \cos(\beta-\alpha), m_{A^0}]$ in each 2HDM
are derived for $m_{A^0} > 225$ GeV. In this work we consider the scenario of
inverted hierarchy with $m_{h^0}<125$ GeV and $m_{H^0}=125$ GeV in which the
decay $A^0\to h^0 Z^{(*)}$ (i.e. including the case of an off-shell $Z$) can
have a large branching ratio in the 2HDM (Type I) for $m_{A^0}<225$ GeV. We
calculate the signal cross section $\sigma(gg\to A^0)\times {\rm BR}(A^0\to
h^0Z^{(*)})\times {\rm BR}(h^0\to b\overline b)$ in the 2HDM (Type I) with NFC
and compare its magnitude with the cross section for the case of normal
hierarchy ($m_{h^0}=125$ GeV) that is currently being searched for at the LHC.
For the experimentally unexplored region $m_{A^0} < 225$ GeV it is shown that
the above cross section for signal events in the scenario of inverted hierarchy
can be of the order of a few picobarns. Such sizeable cross sections are
several orders of magnitude larger than the cross sections for the case of
normal hierarchy, thus motivating an extension of the ongoing searches for
$A^0\to h^0 Z^{(*)}$ to probe the scenario of inverted hierarchy.
