Interesting Question but honestly I do not know about the details of the overlap but I can still help you by suggesting this book A Tale of Two Revolts: India's Mutiny & the American Civil War by Rajmohan Gandhi.

After visiting the British Library East India Archives in London for my dissertation/thesis on the Mutiny I can tell you that there was a little information overlapping both wars. One that really stuck with me was after the Mutiny in India the army and navy were reformed to deal with the possibility of another revolt in the subcontinent. An inspector for the navy commented (paraphrased) "the state of the Indian navy is so bad that if they came into conflict with American ships they would be completely outmatched by the Americans and their dalgreen guns."