Autism spectrum disorder (ASD) is a neurodevelopmental disease characterized by emotional and social deficits, which can be associated with sympathetic dysregulation. Thus, we aimed to analyze the electrodermal activity (EDA) using time, and novel spectral and nonlinear indices in ASD. The cohort consisted of 45 ASD boys and 45 age-matched controls. EDA was continuously recorded at rest. The EDA indices were evaluated by time-, spectral-, and nonlinear-domain analysis. Our results revealed increased non-specific skin conductance responses, spectral parameters in high and very-high frequency bands, approximate and symbolic information entropy indicating sympathetic overactivity in ASD vs. controls (p < 0.05, for all). Surprisingly, the nonlinear index from detrended fluctuation analysis α1 was lower in ASD vs. controls (p = 0.024) providing thus distinct information about qualitative features of complex sympathetic regulation. Concluding, the complex time, spectral, and nonlinear EDA indices revealed discrete abnormalities in sympathetic cholinergic regulation as one of the potential pathomechanisms contributing to cardiovascular complications in ASD.