Solar wind protons can charge exchange with the extensive hydrogen corona of Mars, resulting in a significant flux of energetic neutral atoms (ENAs). As these solar wind hydrogen ENAs precipitate into the upper atmosphere, they can experience electron attachment or detachment, resulting in populations of H− and H+, respectively, with upstream velocity. We seek to characterize the behavior of H− in the ionosphere of Mars through a combination of in situ data analysis and mathematical models. Observations indicate that measurable H− precipitation in the ionosphere of Mars is rare, occurring during only 1.8% of available observations. These events occur primarily during high energy solar wind conditions near perihelion. We also compare H− fluxes to those of H+ and find that H− fluxes are ∼4.5 times less than H+, indicating preferential conversion of hydrogen ENAs to H+. We develop a simple model describing the evolution of the charged and neutral fraction of ENAs and H− ions versus altitude. We find that 0.29 - 0.78% of ENAs are converted to H− for solar wind energies 1 - 3 keV. We also predict that the effects of photodetachment on the H-H− system are non-negligible.