  Observations of molecular hydrogen (H$_2$) fluorescence are a potentially
useful tool for measuring the H$_2$ abundance in exoplanet atmospheres. This
emission was previously observed in M$\;$dwarfs with planetary systems.
However, low signal-to-noise prevented a conclusive determination of its
origin. Possible sources include exoplanetary atmospheres, circumstellar gas
disks, and the stellar surface. We use observations from the "Measurements of
the Ultraviolet Spectral Characteristics of Low-mass Exoplanet Host Stars"
(MUSCLES) Treasury Survey to study H$_2$ fluorescence in M$\;$dwarfs. We detect
fluorescence in Hubble Space Telescope spectra of 8/9 planet-hosting and 5/6
non-planet-hosting M$\;$dwarfs. The detection statistics, velocity centroids,
and line widths of the emission suggest a stellar origin. We calculate
H$_2$-to-stellar-ion flux ratios to compare flux levels between stars. For
stars with planets, we find an average ratio of 1.7$\,\pm\,$0.9 using the
fluxes of the brightest H$_2$ feature and two stellar C IV lines. This is
compared to 0.9$\,\pm\,$0.4 for stars without planets, showing that the
planet-hosting M$\;$dwarfs do not have significant excess H$_{2}$ emission.
This claim is supported by the direct FUV imaging of GJ 832, where no
fluorescence is observed at the expected star-planet separation. Additionally,
the 3-$\sigma$ upper limit of 4.9$\,\times\,$10$^{-17}$
erg$\;$cm$^{-2}\;$s$^{-1}$ from these observations is two orders of magnitude
below the spectroscopically-observed H$_2$ flux. We constrain the location of
the fluorescing H$_2$ using 1D radiative transfer models and find that it could
reside in starspots or a $\sim$2500-3000$\;$K region in the lower chromosphere.
The presence of this emission could complicate efforts to quantify the
atmospheric abundance of H$_2$ in exoplanets orbiting M$\;$dwarfs.
