I did a search on www.civilwardata.com. No record of him serving CT. I did find the following "Nichols" possibles; USA, all states 42 Joseph, 3 Joseph H., zero J. and 1 J.H. CSA, all states; 14 Joseph, zero Joseph H., 9 J. and 6 J.H., for a total of 75 possibles. I think unless you can provide more details, such as what was his civilian occupation, it would be very difficult to determine if he is one of these individuals.

A better possibility is to see if a pension was given for his service. I don't have pension records, but someone else might be able to track this.