  A phenomenological study for determining the chirality structure in
lepton-flavor-violating Higgs (hLFV) decays $h \to \tau\mu$ at the LHC is
presented. We estimate the effects of the $\tau$ polarization in the analysis
andthe importance of determining the relative visible momentum ratio $x$, and
show the analysis with a collinear mass $m_{col1}$ by assuming one missing
particle is appropriate. We find that the sensitivity would be generically
affected up to $\pm$ $4-6$~\% in terms of the BR$(h\to \tau\mu)$ upper bound,
and show the altered bounds on the $(|y_{\mu\tau}|, |y_{\tau\mu}|)$ plane. We
further study the benchmark scenarios, and demonstrate the sensitivity study
for the chirality structure using the relative visible momentum ratio. We find
that the two fully polarized cases, the $\tau_R$ and $\tau_L$ scenarios
consistent with the recently reported excess, are distinguishable at 2$\sigma$
level for 1000~fb$^{-1}$. We also show that a further improved study
potentially provides a similar sensitivity already for 139~fb$^{-1}$.
