The dynamical state of cortical neural activity constrains the complexity of functions it can perform. A marginally stable dynamical state – called criticality – is thought to be beneficial for brain functions that require multiple time scales, broad dynamic range, and large information storage and transmission. A growing body of evidence suggests that criticality is a feature of healthy brain dynamics, but breaks down in certain brain disorders.  Here we ask whether Parkinson’s disease incurs deviation from criticality compared to healthy controls.  We analyze human resting state EEG activity in primary motor cortex. Parkinson’s patients exhibit prominent oscillatory brain activity in multiple frequency bands (low delta and high theta) that is not present in controls.  Surprisingly, we find that these emergent oscillations are close to criticality, i.e., amplitude fluctuations with approximate temporal scale invariance.  We compare traditional signatures of criticality and more principled measurements of proximity to criticality using our recently developed approach based on temporal renormalization group theory and information theory. Our new approach and traditional methods agree, suggesting that critical dynamics are not always healthy; Parkinson’s disease is associated with the emergence of near critical oscillations in motor cortex.