  The latest LHC data confirmed the existence of a Higgs-like particle and made
interesting measurements on its decays into $\gamma \gamma$, $Z Z^\ast$, $W
W^\ast$, $\tau^+ \tau^-$, and $b \bar{b}$. It is expected that a decay into $Z
\gamma$ might be measured at the next LHC round, for which there already exists
an upper bound. The Higgs-like particle could be a mixture of scalar with a
relatively large component of pseudoscalar. We compute the decay of such a
mixed state into $Z \gamma$, and we study its properties in the context of the
complex two Higgs doublet model, analysing the effect of the current
measurements on the four versions of this model. We show that a measurement of
the $h \rightarrow Z \gamma$ rate at a level consistent with the SM can be used
to place interesting constraints on the pseudoscalar component. We also comment
on the issue of a wrong sign Yukawa coupling for the bottom in Type II models.
