In this play, the two women know each other but are not close friends. Mrs. Peters is the wife of the sheriff and she lives in town. She is considered "married to the law" and didn't grow up in the area, making her a bit of an outsider. Her story about the boy who killed her kitten with a hatchet in front of her helps us understand as readers how much she identifies with Mrs. Minnie Wright and her seeking revenge over her murdered canary.
Mrs. Hale and Minnie Wright were life-long friends. They both grew up in the area, went to school together, and have similar lives. Mrs. Hale feels guilt and regret for not visiting Minnie more often and perhaps, by being a better friend, she could have helped prevent the murder of John Wright.
They are connected by their gender and by the feelings they share every time the men make some silly comment about women's work and the unimportance of it all. In fact, the important evidence is indeed found among the "unimportant" kitchen things that the men dismiss.
Despite the differences of these two women, they silently agree to hide the evidence that would prove Minnie Wright's guilt by putting the dead bird wrapped in silk cloth in Mrs. Hale's coat pocket instead of sharing what they've found with the men.
Like all the characters in this play - all the residents in this fictional town - there is a reserve that exists between these two woman. They are focused on their own home life and so do not form a bond between them. In addition, Mrs. Peters is an outsider and did not grow up with Minnie or Mrs. Hale - therefore, she is further removed from the situation and from her fellow wife.
This separation between these two women is echoed in Minnie's situation and the cause for the conflict of the story, the murder of her husband. Minnie has been separated from others, at the mercy of her husband alone. She is isolated, lonely, and unprotected. She lives "down in the hollow" and is far removed from other homes. This sets up the bad situation in her marriage, which leads to her retaliation.
The relationship between the two characters changes throughout the play, however. One of the themes of this story is that of gender roles, and the way Mrs. Peters and Mrs. Hale grow closer as they try to understand and protect Minnie shows these gender roles. As women, they understand the difficulty Minnie was facing and the intensity of her subjugation. This is why the decide, together, to conceal the evidence of Minnie's guilt, forming a bond in their mutual decision - female against male.