We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of nonoverlapping resonances. The results are derived in the framework of random matrix theory and hold more generally for any chaotic quantum system that is weakly coupled to the continuum. The "correlation hole" that characterizes the spectral autocorrelation in the bound molecule diminishes as the typical average total width of a resonance increases.