It is generally accepted that the basal ganglia play an important role in interval timing that requires the measurement of temporal durations. By contrast, it remains controversial whether the basal ganglia play an essential role in temporal order judgment (TOJ) of successive stimuli, a behavior that does not necessarily require the measurement of durations in time. To address this issue, we compared the effects of idiopathic Parkinson’s disease (PD) on the TOJ of two successive taps delivered to each hand, with the arms uncrossed in one condition and crossed in another. In addition to age-matched elderly participants without PD (non-PD), we examined young healthy participants so that the effect of aging could serve as a control for evaluating the effects of PD. There was no significant difference between PD and non-PD participants in any parameter of TOJ under either arm posture, although reaction time was significantly longer in PD compared with non-PD participants. By contrast, the effect of aging was apparent in both conditions. With their arms uncrossed, the temporal resolution (the interstimulus interval that yielded 84% correct responses) in elderly participants was significantly worse compared with young participants. With their arms crossed, elderly participants made more errors at longer intervals (~1 s) than young participants, although both age groups showed similar judgment reversal at moderately short intervals (~200 ms). These results indicate that the basal ganglia and dopaminergic systems do not play essential roles in tactile TOJ involving both hands and that the effect of aging on TOJ is mostly independent of the dopaminergic systems.