The line profile of the resonance line of K I at 7698 Å has been analyzed in the halo turnoff star HD 84937, using a high-resolution (λ/Δλ = 110,000), high signal-to-noise ratio (S/N = 550) spectrum. Three different groups have reported detecting ⁶Li in this star, based on a red asymmetry in the Li I λ6707 line profile (⁶Li displays an isotopic shift of about 0.15 Å to the red, relative to ⁷Li, in this line). It is possible, however, that convection could introduce this red asymmetry by mass motions of ⁷Li in the star's atmosphere. At the metallicity of HD 84937, the K I resonance line at 7698 Å is expected to have a similar line strength to the Li I λ6707 feature, and both these lines are resonance transitions. In addition, both potassium and lithium have similar first ionization potentials. The result of these similarities is that the Li I and K I lines are formed at nearly identical regions in the atmosphere of HD 84937. This study presents a line profile analysis of the K I line, which has negligible isotopic splitting and is effectively a single-component line, in HD 84937. Any possible convective motions of sufficient magnitude to produce a spurious detection of ⁶Li should also produce detectable asymmetries in the K I line. No such asymmetries are found here, strengthening the case that the previously reported detections of ⁶Li in HD 84937 are real.