This story was surprisingly difficult to find: partly because Andreyev apparently wrote quite a number of stories about murderers and/or lunatic asylums, partly because there are so many different English translations of the title of the story.
It's this story, written in 1902 and entitled "Мысль" ("Mysl") in the original Russian - a title which has been variously translated as "Thought", "Mind", "Reason", "A Thought", or "A Dilemma". From the foreword:
Like Hamlet, our hero is "sicklied o'er with the pale cast of thought;" like him, too, he feigns insanity to carry out his subtle schemings, yet here is the vital difference: in spite of his modernity, Dr. Kerzhentseff harks back to the primitive for the motive of his murder. Practically he seeks revenge, while Shakespeare's hero is unquestionably the more noble (and more lovable), for he seeks justice itself. But that is another hair-splitting distinction.
Dr. Kerzhentseff's forceful logic confounds not only himself, but the experts, who inevitably are bound to disagree as to the prisoner's mental status, and the big question to the end remains unanswered.
And some relevant excerpts from the text of the story itself.
His plan to pretend to be mad:
The rôle of a madman did not strike me as being very difficult of enactment. Some of the necessary directions I got from books; others I had to obtain—like any actor worthy of the name—through my own creative faculty; the rest had to be left to be recreated by the public itself, whose emotions had been developed through constant contact with books and the theatre, where, by means of two or three vague contours, it had been taught to recreate live types.
The murder itself:
The hand of Alexis remained where it was, while he, pale, still keeping his eyes upon me, smiled incredulously with his lips alone. Tatiana Nikolayevna uttered a strange cry, but it was too late. I struck him with the sharp edge nearer the temple than the eye. And when he fell I bent over and struck him two more times. The district attorney declared that I had struck him several times, because his head was badly crushed. But that is untrue. I struck him only three times: once when he was standing, and twice on the floor.
His first thought that he might truly be mad:
My eyelids began to grow heavy, and I wanted to sleep, when languidly, very simply, like the other thoughts, there entered into my head a new thought, dominating with all the qualities of my thought: clearness, preciseness and simplicity. Languidly it entered and remained. Here it is, speaking, as it were, in the third person:
"It is very possible that Dr. Kerzhentseff is really insane. He thought that he simulated, but he is really insane—insane at this very instant."
From near the very end of the story:
And I, Dr. Kerzhentseff, shall prove that. I will simulate normality. I will attain freedom. I will spend the remainder of my life in learning.
All quotes are from the John Cournos translation, first published in 1910 and freely available from Wikisource on the page linked above.
How I found it:
it took many attempts, but the successful Google search terms were "leonid andreyev story murder pretend insane asylum
". That led me to these
, both of which were about the Czech writer Kohout
, one of whose plays drew heavily on this particular Andreyev story. Then the problem was to find the text (or even a synopsis or review) of the story, for which I needed to try many different alternative translations of the title. Eventually I found the Wikisource page linked above.