Nonlinear interactions between different components of multiwavelength radiation are one of the main processes shaping properties of quasi-CW fiber lasers. In random fiber lasers, nonlinear influence may be more complicated, as there are no distinct longitudinal modes in radiation because of the random nature of the feedback. In this Letter, we experimentally characterize internal correlations in the radiation of a multiwavelength random distributed feedback fiber laser. An analysis of Pearson correlation functions allows us to spatially locate the area over the fiber laser length in which correlations are more likely to occur. This, in turn, leads us to the conclusion about the main mechanism of spectral correlations—the relative intensity noise transfer from the pump wave.