But back to the OP. Religion was, initially, the best guess on how the universe works. As such, many of the initial stages in science were developed in a religious context.
But, as we gained more information and experience, we realized that the religious answers didn't work any longer.
There were two basic responses of religion to this: ignore it, or change the religious beliefs to adapt to the new information. But religious views, per se, stopped being a fundamental driving force for the development of science and our understanding of the world around us.
This also gets to the basic difference between religion, which is faith based, and science, which is evidence based. For science, any notion that cannot be tested, even in theory, is considered to be irrelevant. That is because evidence is what determines what is and what is not science. Religion, on the other hand, uses faith as its central value. That means that many untestable ideas are accepted and promoted. This is the basic disconnect between the two realms of investigation.
So, are they correlated? The question itself is a bit strange, but initially they were positively correlated. Now they tend to be negatively so.