  We study possible new physics interactions in the $ZZH$ vertex contributing
to the Higgsstrahlung process $e^+ e^- \to ZH$ at proposed future $e^+e^-$
colliders using the polarization of the $Z$ as a probe. We calculate the spin
density matrix of the $Z$ for the process and determine the eight independent
polarization parameters of the $Z$ boson which have the potential to constrain
the anomalous couplings. We study angular asymmetries using the decay leptons
from the $Z$ boson which are simply related to the polarization observables. We
also estimate the limits that can be placed on the anomalous couplings using
measurements of these angular asymmetries at centre of mass energies of 250 GeV
and 500 GeV and various combinations of polarized $e^+$ and $e^-$ beams.
