Research on the impact of neurocognitive disorders on rhythmic abilities has yielded mixed results. Additionally, rhythm perception without production has not yet been evaluated. In this study, eighty-seven patients (mean age = 81) participated and underwent an evaluation of beat perception and sensorimotor synchronisation with three levels of beat saliency (BS) (metronome; high-BS music; low-BS music). We hypothesised that beat perception and production would be influenced by cognitive status, and that in the tapping task, this might depend on beat saliency. Synchronisation was most consistent with a metronome, followed by high-BS music, and low-BS music (p < .001). Consistency decreased with lower mini-mental state examination (MMSE) scores, particularly with low-BS music (p < .001). Lower MMSE scores predicted beat perception deficits (p < .05). Finally, individuals with lower MMSE tended to have slower spontaneous tempo (p < .05). Performance on an inhibition task was negatively associated with synchronisation consistency for both types of music (p < .05). In summary, synchronisation with an auditory signal with a clear beat was the only task not dependent on cognitive status, whereas all other perception and production tasks were dependent on MMSE scores.