I am a direct descendant on my father's side of Lydia Bassett Gilbert who was hung at Hartford in about 1655.
The expert on the CT witchcraft hysteria is John Demos, a history professor at Yale. He wrote a book available in paper back "The Enemy Within" in which he discusses both the Hartford and the Salem witch hysterias.
He focuses on two of my direct ancestors, Lydia Gilbert and Rebecca Nurse, as examples of women who were hung without any justification (not to imply that any of them had any justification, it's just that some of the accused in Hartford and Salem were "the usual suspects", i.e. bitchy women, widows, who has pissed off people and/or were descended from women rumored to be witches).
I just looked in the index to the Demos book and see no mention of a Barnes. Another source may be the Connecticut Historical Society.
I tried to research Lydia Gilbert's trial, etc. but there were very few records preserved. In fact, until I read the Demos book I wasn't even sure she was hanged. She was and her husband remarried in 8 months and moved to MA.