  Higgs boson properties could be studied with a high accuracy at a muon
collider via the s-channel resonant production. We consider the situation where
the center-of-mass energy of the muon collider is off the resonance above the
Higgs mass. We discuss the discovery potential for a generic heavy Higgs boson
($H$) and compare different production mechanisms, including the "radiative
return" ($\gamma H$), $Z$-boson associated production ($ZH$) and heavy Higgs
pair production ($HA$). These production mechanisms do not sensitively rely on
a priori knowledge of the heavy Higgs boson mass. We include various types of
Two Higgs Doublet Models for the comparison. We conclude that the radiative
return process could provide an important option for both the heavy Higgs
discovery and direct measurement of invisible decays at a high energy muon
collider.
