  We explore the use of polarized $e^+/e^-$ beams and/or the information on
final state decay lepton polarizations in probing the interaction of the Higgs
boson with a pair of vector bosons. A model independent analysis of the process
$e^+ e^- \to f \bar f H$, where $f$ is any light fermion, is carried out
through the construction of observables having identical properties under the
discrete symmetry transformations as different individual anomalous
interactions. This allows us to probe an individual anomalous term independent
of the others. We find that initial state beam polarization can significantly
improve the sensitivity to CP-odd couplings of the $Z$ boson with the Higgs
boson ($ZZH$). Moreover, an ability to isolate events with a particular $\tau$
helicity, with even 40% efficiency, can improve sensitivities to certain $ZZH$
couplings by as much as a factor of 3. In addition, the contamination from the
$ZZH$ vertex contributions present in the measurement of the trilinear
Higgs-$W$ ($WWH$) couplings can be reduced to a great extent by employing
polarised beams. The effects of initial state radiation (ISR) and
beamstrahlung, which can be relevant for higher values of the beam energy are
also included in the analysis.
