Infrared-optical double resonance excitation of hydrogen peroxide using the v3 + v5 and V2 + v5 combination bands as intermediate levels prepares reactant molecules in single rotational states near the OO dissociation threshold. The band origins of the DELTA-upsilon-OH = 4 vibrational overtone transitions originating from these combination bands provide information on the anharmonicities between the OH stretch and the OO stretch and OOH bend, respectively. At low resolution the vibrational overtone transitions are clearly parallel bands of a near prolate symmetric top and can be assigned to zeroth-order J and K quantum numbers. At 0.1 cm-1 resolution the individual features in the vibrational overtone spectra appear as clumps of sharp lines centered at the frequencies of the zeroth-order symmetric top transitions. The number of components within a clump appears to be less than the total number of available vibrational states. The narrowest feature observed has a linewidth of 0.12 cm-1 and sets a lower bound of approximately 35 ps on the lifetime of the dissociating molecule. As J increases from 1 to 21, the clumps of lines coalesce into a smooth Lorentzian envelope. The overall clump width decreases with J, reaching an asymptotic value of 0.67 cm-1 at J congruent-to 17. A model incorporating a J dependent density of bath levels that couple to the zeroth-order bright state predicts the observed changes in the vibrational overtone transitions with J. The rotationally resolved vibrational overtone spectra provide information on the time scale for the conservation of K of the dissociating molecule.