Dual-task (DT) paradigms have been used in gait research to assess the automaticity of locomotion, particularly in people with Parkinson's disease (PD). In people with PD, reliance on cortical control during walking leads to greater interference between cognitive and locomotor tasks. Yet, recent studies have suggested that even healthy gait requires cognitive control, and that these cognitive contributions occur at specific phases of the gait cycle. Here, we examined whether changes in gait stability, elicited by simultaneous cognitive DTs, were specific to certain phases of the gait cycle in people with PD. Phase-dependent local dynamic stability (LDS) was calculated for 95 subjects with PD and 50 healthy control subjects during both single task and DT gait at phases corresponding to (1) heel contact-weight transfer, (2) toe-off-early swing, and (3) single-support-mid swing. PD-related DT interference was evident only for the duration of late swing and LDS during the heel contact-weight transfer phase of gait. No PD-related DT costs were found in other traditional spatiotemporal gait parameters. These results suggest that PD-related DT interference occurs only during times where cortical activity is needed for planning and postural adjustments. These results challenge our understanding of DT costs while walking, particularly in people with PD, and encourage researchers to re-evaluate traditional concepts of DT interference.