The New York Times has a detailed article about this kid's circumstances (I think it was posted here on FR today, but I don't have the reference). There was good reason for this kid to be situationally depressed. His father committed suicide and his mother was permanently disabled from a car accident caused by his drunk cousin who was killed. His mother couldn't care for him, so he had to leave the city to live with grandparents in the far country -- which could have by itself been traumatic.
That being said, it is not the school's business to get into psychiatry. Articles I've seen that blame the school for not "catching on" to the possibility of his actions are ridiculous. If schools could teach kids how to read & write & do math first then I might be open to the idea of school-provided health screening, but it's a very very long shot.
The New York Times, eh? A bleeding-heart liberal rag just trying to put the blame everywhere than where it belongs. My four year old knows that it's WRONG to kill or hurt someone!!