  Observations of the neutral atomic hydrogen (HI) gas in galaxies are
predominantly spatially unresolved, in the form of a global HI spectral line.
There has been substantial work on quantifying asymmetry in global HI spectra
(`global HI asymmetry'), but due to being spatially unresolved, it remains
unknown what physical regions of galaxies the asymmetry traces, and whether the
other gas phases are affected. Using optical integral field spectrograph (IFS)
observations from the Sydney AAO Multi-object IFS (SAMI) survey for which
global HI spectra are also available (SAMI-HI), we study the connection between
asymmetry in galaxies' ionised and neutral gas reservoirs to test if and how
they can help us better understand the origin of global HI asymmetry. We
reconstruct the global H$\alpha$ spectral line from the IFS observations and
find that, while some global H$\alpha$ asymmetries can arise from disturbed
ionised gas kinematics, the majority of asymmetric cases are driven by the
distribution of H$\alpha$-emitting gas. When compared to the HI, we find no
evidence for a relationship between the global H$\alpha$ and HI asymmetry.
Further, a visual inspection reveals that cases where galaxies have
qualitatively similar H$\alpha$ and HI spectral profiles can be spurious, with
the similarity originating from an irregular 2D H$\alpha$ flux distribution.
Our results highlight that comparisons between global H$\alpha$ and HI
asymmetry are not straightforward, and that many global HI asymmetries trace
disturbances that do not significantly impact the central regions of galaxies.
