  It is argued that, in $H \to $ invisibles searches with $Z(\ell\ell)H$
associated production at the LHC, the signal efficiency can be sensibly
improved via a detailed study of the $Z$ boson polarization, discriminating
between the signal and the dominant-irreducible $Z(\ell\ell)Z(\nu\nu)$
background. We first present a comprehensive polarization study, obtaining the
complete set of angular coefficients $A_i$ in the Collins-Soper reference frame
and identifying the dominant phenomenological effects. Then, we show the
results for a realistic Monte Carlo study to $H\to$ invisibles, taking the
polarization analysis into account. We obtain about $20\%$ improvement in the
upper bound for the branching ratio of the Higgs boson to invisible particles,
assuming $300\ \mathrm{fb}^{-1}$ of data at the 13 TeV LHC.
