It depends on what you mean by research. Do you mean something that can be published in a journal or something that is a class assignment? A good topic might be examining the story from a feminist critical perspective and discuss the attitudes of women in the US in the early 20th century. You can examine the men's conversations and the conversations between the women. You could also examine how a story can be transcribed to the theatre as the story was made into a play called "Trifles." You could examine the dramatic elements that are present or not present in the narrative version.