Interactions between objects inside living cells are often investigated by looking for colocalization between fluorescence microscopy images that are recorded in separate colours corresponding to the fluorescent label of each object. The fundamental limitation of this approach in the case of dynamic objects is that coincidental colocalization cannot be distinguished from true interaction. Instead, correlation between motion trajectories obtained by dual colour single particle tracking provides a much stronger indication of interaction. However, frequently occurring phenomena in living cells, such as immobile phases or transient interactions, can limit the correlation to small parts of the trajectories. The method presented here, developed for the detection of interaction, is based on the correlation inside a window that is scanned along the trajectories, covering different subsets of the positions. This scanning window method was validated by simulations and, as an experimental proof of concept, it was applied to the investigation of the intracellular trafficking of polymeric gene complexes by endosomes in living retinal pigment epithelium cells, which is of interest to ocular gene therapy.