  Current experiments do not support, as ATLAS and CMS collaborations at the
Large Hadron Collider reported, that the Higgs-like resonance discovered in
July 2012 is a pure CP-odd state. We examine a general $hZZ$ vertex which
contains CP-even and CP-odd couplings, by studying the process $h\to ZZ^*\to
l_1^+l_1^-l_2^+l_2^-$ with $l_1,\, l_2= e$ or $\mu$, to explore the CP mixed
property of the Higgs-like particle. One momentum asymmetry and two angular
asymmetries have been analyzed in order to reveal the difference from different
CP-couplings. Our study shows that these asymmetries could be interesting
observables in the future precise experiments.
