  The future muon collider has the potential to discover feebly interacting
particles in a wide range of masses above the electroweak scale. It is
particularly suitable to search for heavy neutral leptons (HNLs), as their
production cross section $\sigma \sim m_W^{-2}$ is not suppressed by the new
physics scale. We demonstrate that the muon collider, with the capacity to
observe up to $10^5$ events in the previously unexplored TeV mass range,
provides the means to measure the fraction of lepton number violating (LNV)
processes with precision at the level of a percent. This capability enables
elucidating the nature of HNLs, allowing us to differentiate between Majorana,
Dirac, and non-minimal scenarios featuring multiple degenerate HNLs. We link
the observed fraction of LNV processes to the parameters of the model with
three degenerate HNLs, which could be responsible for generating baryon
asymmetry in the Universe. Additionally, we present a simple estimate for the
number of signal events, as well as analyze the feasibility of vector boson
fusion processes in searches for HNLs.
