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The production of a Higgs boson in association with a $Z$ at anelectron-positron collider is one of the cleanest methods for the measurementof the couplings of the Higgs boson. In view of the large production crosssection at energies a little above the threshold, it seems feasible to make amore detailed study of the process by measuring the cross sections forpolarized $Z$ in order to measure possible anomalous $ZZH$ couplings. We showthat certain combinations of cross sections in $e^+e^- \to ZH$ with different$Z$ polarizations help to enhance or isolate the effect of one of the two kindsof $ZZH$ couplings possible on general grounds of CP and Lorentz invariance.These combinations can be useful to get information on the $ZZH$ coupling inthe specific contexts of an effective field theory, two-Higgs-doublet models,and composite Higgs models, in a relatively model-independent fashion. We findin particular that the longitudinal helicity fraction of the $Z$ is expected tobe insensitive to anomalous couplings, and would be close to its value in thestandard model in the scenarios we consider. We also discuss the sensitivity ofthe proposed measurements to the anomalous couplings.

Polarized $Z$ cross sections in Higgsstrahlung for the determination of anomalous $ZZH$ couplings