The time development of both hard X-ray emission and soft X-ray nonthermal line widths is important for an understanding of energy transport in the flaring solar corona. In this Letter, we investigate the relationship between the temporal behavior of these two phenomena for a number of flares detected by instruments on the Yohkoh spacecraft. We examine 10 flares, all occurring within 30° of the limb, using data from the Bragg Crystal Spectrometer (BCS) and the hard X-ray telescope (HXT). We find that the nonthermal velocity either (1) exhibits a maximum prior to the first significant burst of hard X-rays or (2) is already decaying from an earlier unobserved maximum at the time of the first significant burst of hard X-rays. The decay of the nonthermal velocity as it proceeds from its observed maximum shows little evidence for a direct association with individual hard X-ray bursts. These observations suggest that the nonthermal broadening may be a direct consequence of the flare energy release process rather than a by-product of the energy deposition. In addition, the attainment of a maximum in the nonthermal line width very early in the flare is more indicative that plasma turbulence is the source of the observed broadening rather than hydrodynamic flows, such as chromospheric evaporation.