What is the crises in "Utterly Perfect Murder", written by Ray Bradbury?

I am not sure I have a completely clear idea of what you mean by "crisis," but I'll see what I can do.

There are two possible definitions for "crisis" that could apply to this story:

• an unstable situation of extreme danger or difficulty; "they went bankrupt during the economic crisis"


• a crucial stage or turning point in the course of something; "after the crisis the patient either dies or gets better"

I am going to guess that you are basing your question on the second definition, and that what you are asking is very similar to the question "What is the conflict in the story "Utterly Perfect Murder."  Conflict is a more common literary term for what I think you are asking.

In this story, the main character, Doug, decides to kill his childhood arch-enemy for treating him badly as a kid.  It is tempting to see something of the conflict in this...after all, Ralph did the following:

Remember how he hit my arm? Bruises. I was covered with bruises, both arms; dark blue, mottled black, strange yellow bruises.

And I recalled one spring when I came to school in a new tweed knicker suit and Ralph knocking me down, rolling me in snow and fresh brown mud.

"Well," said Ralph, "I'll give you my extra Tarzan statue if you'll give me that catcher's mitt." Fool! I thought. The statue's worth twenty-five cents. The glove cost two dollars! No fair! Don't! But I raced back to Ralph's house with the glove and gave it to him... My brother didn't find out about his catcher's mitt and the statue for two weeks, and when he did he ditched me when we hiked out in farm country and left me lost because I was such a sap.

So you can see some examples of the "conflict" between the boys.  But is this the conflict of the story?  I don't think so.  It's not the "heart" of the story.  That comes later.  When he gets to Doug's house for the purpose of shooting him, he can't do it.  Doug is a shriveled old man, no longer powerful, no longer able to intimidate him.  He leaves, saying the following:

"Bang," I whispered. "Bang. Bang. Bang. Bang. Bang." His body shook with the impact. "You're dead. Oh, God, Ralph, you're dead." I turned and walked down the steps and reached the street before he called: "Doug, is that you?" I did not answer, walking.

The real conflict of the story is between Ralph and himself. He has to put his feelings about the past away.  He has to reclaim the strength that he thought Doug had taken away during his early years.  The "crisis moment" is when Doug opens the door and Ralph stands facing him, eyeball to eyeball, for the first time in a long time.  That's the moment when Ralph realizes that he could walk "back toward Now and Today for the rest of my life."