Background: This study aimed at answering the following research questions: (1) Does the self-reported level of sensory-processing sensitivity (SPS) correlate with complexity, or criticality features of the electroencephalogram (EEG)? (2) Are there significant EEG differences comparing individuals with high and low levels of SPS? Methods: One hundred fifteen participants were measured with 64-channel EEG during a task-free resting state. The data were analyzed using criticality theory tools (detrended fluctuation analysis, neuronal avalanche analysis) and complexity measures (sample entropy, Higuchi’s fractal dimension). Correlations with the ‘Highly Sensitive Person Scale’ (HSPS-G) scores were determined. Then, the cohort’s lowest and the highest 30% were contrasted as opposites. EEG features were compared between the two groups by applying a Wilcoxon signed-rank test. Results: During resting with eyes open, HSPS-G scores correlated significantly positively with the sample entropy and Higuchi’s fractal dimension (Spearman’sρ = 0.22,p< 0.05). The highly sensitive group revealed higher sample entropy values (1.83 ± 0.10 vs. 1.77 ± 0.13,p= 0.031). The increased sample entropy in the highly sensitive group was most pronounced in the central, temporal, and parietal regions. Conclusion: For the first time, neurophysiological complexity features associated with SPS during a task-free resting state were demonstrated. Evidence is provided that neural processes differ between low- and highly-sensitive persons, whereby the latter displayed increased neural entropy. The findings support the central theoretical assumption of enhanced information processing and could be important for developing biomarkers for clinical diagnostics.