Acoustic emission (AE) events were recorded during the peeling of pressure-sensitive adhesive (PSA) tape from a silicate glass surface. The distributions of AE event durations and energies are found to have the form of power laws. Power-law dependencies (hyperbolic distributions) are recognized as a consequence of self-organized criticality (SOC), resulting from the absence of any characteristic length or time scales. In these studies, standard optical microscopy was used to characterize the fractal nature of the PSA-glass interface. The present results suggest that it is the inherent static structural features found at the fractal PSA-glass interface which produce the observed hyperbolic distributions in AE events, rather than a true SOC process.