Suicide does not seem to demand a whodunnit. Still, that is exactly what those left behind are bequeathed. Who exactly was the person who decided that this was the day, the afternoon, the moment in which she or he would bring their life to a full-stop? And how was that person related to the person their family and friends had known and loved?

Jill Bialosky is a poet and book editor in New York. Twenty-five years ago her half-sister Kim, 10 years her junior, gassed herself with the exhaust from her car in the garage of the home she shared with their mother. Kim was 21. The tragic decision she made has shadowed Bialosky’s life and the lives of her other two sisters for all the days and years that have followed. Who could do such a thing?

Bialosky’s memoir is an account of her efforts to find out. She writes with an editor’s rigour, but her quest is by nature a messy, obsessive poet’s kind of lament that tos and fros between her present tense and her sister’s imperfect past. It is the event that transformed the way the author thinks about “intimacy, motherhood, friendship and our responsibilities to others”. It is not one tragedy but many.

Its history seems to begin in other grief – most notably in the death of Bialosky’s own father when her mother was 24, with three daughters under the age of three, the fateful fact that first marked their family as different, as desperate. It projects forwards also, infecting the overwhelming sadness of the author’s first efforts to have a family of her own. Bialosky is just married and pregnant when she hears of Kim’s death. Her baby is born prematurely and dies a few hours after birth. Another pregnancy two years later ends the same way. And all the mourning sickness bleeds into one.

It is not easy to read this history. Bialosky is plagued by the guilt of the survivor. “I believed Kim had been stolen from us as our punishment for not having been aware of how deeply she was suffering.”

She fossicks through her sister’s closets and her diaries in search of clues. The wardrobes yield only a forlorn itemisation of emptiness: “1. Four pairs of black faux-leather boots. 2. One pair white cowboy boots with fringe. 3. Ten pairs of jeans. 4. Laura Ashley bridesmaid dress with cabbage rose print she wore as maid of honour at my wedding… ” The diaries open the inevitable bell jar of private despair.

After Bialosky’s father died, her mother searched for another man to fill their “house of women”. She found one for a while in Kim’s father. They married, but he left and disappeared when Kim was three, only to return sporadically to his daughter’s life a decade later. Kim’s diaries revealed how, like her mother, she tried and failed to make him constant, to make him approve of her, to love her. At 16, Kim was making charts in her journal that analysed “What would you give for a person you loved” – a list that ran: “Loyalty, my life, myself”. Her first true boyfriend proved unfaithful and ended their relationship months before she died.

Is this enough to explain what happened? Bialosky doesn’t know. She reads between the lines of all the literature of self-annihilation with a forensic eye, from Virginia Woolf’s suicide note to Sylvia Plath’s poem Tulips. She seeks out Dr Edwin Shneidman, who invented the science of suicidology, and has him look at her sister’s case. She joins a support group of relatives of suicides and listens to endless stories just like, but quite unlike, her own. Some of it comes back to simple statistics. Kim’s was an early spring death. As Bialosky discovers, when TS Eliot observed that “April is the cruellest month” he was factually precise. The “mixing of memory and desire” sees a 12% spike in suicides compared with the rest of the year. Was her sister just a victim of the season? In response to the questions of her adopted son, Lucas, light of her life, Bialosky can only say: “Now and then life gets too painful and a person can’t see out of it, can’t let anyone inside, and that’s what happened to Kim.”

The suicidologist, Dr Shneidman, when Bialosky gets to see him, appears to speak not of verifiable certainties but in the language of fiction. Kim’s father was “the villain of the piece” who resented her arrival, and because he chose not to see her, taught her “she was not worthy”. She was, he says, “star-crossed” to her fate. Shneidman can read Kim’s life like a book; but, inevitably, it’s a book that is not remotely as honest and insightful and inconclusive as this one.

Samaritans: 08457 90 90 90 (24-hour national helpline)

History of a Suicide is published by Granta, £16.99. Click here to buy it for £13.59