  As the planning stages for a high energy muon collider enter a more concrete
era, an important question arises as to what new physics could be uncovered. A
TeV-scale muon collider is also a vector boson fusion (VBF) factory with a very
clean background, and as such it is a promising environment to look for new
physics that couples to the electroweak (EW) sector. In this paper, we explore
the ability of a future TeV-scale muon collider to search for Majorana and
Dirac Heavy Neutral Leptons (HNLs) produced via EW bosons. Employing a
model-independent, conservative approach, we present an estimation of the
production and decay rate of HNLs over a mass range between 200 GeV and 9.5 TeV
in two benchmark collider proposals with $\sqrt{s}=3,\,10$ TeV, as well as an
estimation of the dominant Standard Model (SM) background. We find that
exclusion limits for the mixing between the HNLs and SM neutrinos can be as low
as $\mathcal{O}(10^{-6})$. Additionally, we demonstrate that a TeV-scale muon
collider allows for the ability to discriminate between Majorana and Dirac type
HNLs for a large range of mixing values.
