It has been suggested that the complexity of the brain is closely related to its state of consciousness. The perturbational complexity index (PCI) has been used in humans and rodents to distinguish conscious from unconscious states based on the global cortical responses (recorded by electroencephalography; EEG) to local cortical stimulation (CS). However, it has been unclear how different cortical layers respond to CS and contribute to the resulting intra- and inter-areal cortical communication and PCI. A detailed investigation of these local dynamics is needed to understand the basis for PCI. We hypothesized that the complexity level of global cortical responses (PCI) corresponds to variations in layer-specific activity and connectivity patterns. We investigated global cortical dynamics and layer specific activity in mice, combining cortical electrical stimulation, global EEG, and local multi-electrode, laminar recordings from layers 1-6 in somatosensory cortex, during wakefulness and general anesthesia (sevoflurane). We found that transition from wake to sevoflurane anesthesia correlated with a drop in global and local PCI values (complexity). This was accompanied by a local decrease in neural firing rate, spike-field coherence, and long-range functional connectivity specific to deep layers (L5, L6). Our results suggest that deep cortical layers are mechanistically important for changes in PCI, and thereby for variations in the states of consciousness.