Clare's actual cause of death is ambiguous in the text. When she falls out of the window, she could have been pushed by Irene or by John (Clare's husband), or she could have thrown herself out of the window. The ambiguity of Clare's death highlights the idea that her death is multiply determined and is in part caused by the cultural construction of race and gender. Clare is of biracial ancestry but looks and passes for white. The cultural construction of race means that she is classified as black according to the one-drop rule (the idea that someone with even one drop of black "blood" or ancestry can't be white) but passes as white to have access to the privileges that being white in a racist society can bring. In addition, her gender resigns her to having to get access to privilege through men (such as her white husband, John).

In the end, Clare is caught between these inflexible distinctions. She isn't white according to the rules of the society at the time, but her husband is a racist who would likely kill her if he knew she had black ancestry. Irene, who is black and identifies as black, perhaps wants to kill Clare for her own reasons. Clare offends her sense of racial pride and is also having an affair with Irene's husband. Clare is herself caught in her lie. If the social construction of race were more fluid, she would not have to identify strictly as white or black and likely would not have met this tragic end.

Your question hits upon the crux of the meaning of Larsen's story: What is the responsibility that can be assigned for what happens to Clare? In a moral sense, Clare is responsible for her own end, her own death, because she chose to enact a charade that entrapped herself and others in untenable and even dangerous, as we ultimately see, situations where compromised integrity is the foundational premise for all: Irene, John, Brian, Clare. In a situational sense, John Bellow, Clare's husband, is responsible for Clare's death because of his violent intrusion at the peaceable party and because of his threatening approach toward Clare. A case can also be made that Brian Redfield bears some moral responsibility because he allows himself to be won away toward affection for Clare, bearing in mind that Brian and Irene share the name "Redfield": red (bloody)-field (blood-covered area).

Brian had gone out. She turned her face into her pillow to cry. But no tears came.

While the resolution, the ending, of the story is often called "ambiguous," one analysis renders the ending more of a "surprise" ending than an ambiguous one because of the clues that are given by Larsen as to Irene's ultimate active responsibility for Clare's death: "If Clare should die! ... to wish that ... [and] not get rid of it."  With it in mind that Larsen does indicate responsibility through textual clues --like Irene's musings over her fate if...