I think you are asking about quite a high-level definition of "correlated", and this is obviously going to depend on the particular context or stimulus. That is, knowledge about thunder and lightning allows us to infer that they have a common cause, even though perceptually they can be decoupled (that is, we don't perceive them as occurring together).
However, I can point you to a few things that speak to the perception of correlation in time. This literature concerns the perception of synchrony between two stimuli, such as a flash (vision) and a beep (audition). For visual-auditory pairings, the window of "temporal synchrony" can be quite imprecise: events can be separated by up to 200 ms and still be judged as having occurred at the same time (see Dixon and Spitz, 1980, and Vatakis and Spence, 2006).
However, with multiple events in the environment and depending on the type of stimulus, sensitivity can improve. The above literature as well as my general reply is sourced from this article by Roseboom et al (2011), which may be a good starting point for further reading if this is where you were going with the question.
- Dixon NF, Spitz L (1980) The detection of auditory visual desynchrony. Perception 9: 719–721.
- Roseboom, W., Nishida, S., Fujisaki, W. & Arnold, D.H. (2011). Audio-visual speech timing sensitivity is enhanced in cluttered conditions. PLoS One, 6, e18309.
- Vatakis A, Spence C (2006) Audiovisual synchrony perception for music, speech, and object actions. Brain Research 1111: 134–142.