  We examine the prospects for measuring the $H Z \gamma$ coupling of a
Standard Model-like Higgs boson with a mass between 120 and 160 GeV at the
future TESLA linear \ee collider, assuming an integrated luminosity of 1
ab$^{-1}$ and a center-of-mass energy of 500 GeV. We consider the Higgs boson
produced in association with $\nu_e \bar{\nu_e}$ via the $W W$ fusion reaction
$e^+e^- \to \nu_e \bar{\nu_e} H$, followed by the rare decay into a $Z$ boson
and a photon, $H \to Z \gamma$. Accounting for all main background
contributions, different selection procedures are discussed. Uncertainties on
the \hZg branching fraction of approximately 48% (27%, 44%) can be achieved in
unpolarised \ee collisions for $M_H$ = 120 (140, 160) GeV. With appropriate
initial state polarisations $\Delta$BF(\hZg)/BF(\hZg), or the precisions on the
\hZg partial width, can be improved to 29% (17%, 27%) and provide valuable
information on the $HZ\gamma$ coupling. We regard our results as a convincing
confirmation of the great potential of a linear collider to access and reliably
measure important parameters of the Higgs boson despite initially overwhelming
background with final state signature similar to the signal events.

High Energy Physics - Phenomenology