I need some evidence to prove whether Holden is insane or not in The Catcher in the Rye.

I agree with the post above that mentions
PTSD.

(Symptoms of PTSD: depression, sleeplessness,
hypervigilance, weeping, negativity, self-isolation, attention deficit and trouble
concentrating, exaggerated startle response, untrollable anger, recurrent invasive
recollections of stressor events)

The book is full of
examples.

First, there are two
stressor events: Allie's death and the death of a classmate, Jame Castle, who leaped out
a dorm window wearing the sweater Holden loaned
him.

Allie's death:

readability="13">

I was only thirteen, and they were going to have
me psychoanalyzed and all, because I broke all the windows in the garage. I don't blame
them. I really don't. I slept in the garage the night he died, and I broke all the
goddam windows with my fist, just for the hell of it. I even tried to break all the
windows on the station wagon we had that summer, but my hand was already broken and
everything by that
time...

Jame's Castle's
death:

So
Stabile, with about six other dirty bastards, went down to James Castle's room and went
in and locked the goddam door and tried to make him take back what he said but he
wouldn't do it. So they started in on him. I won't even tell you what they did to
him--it's too repulsive--but he still wuldn't tke it back, old James Castle. ...a skinny
little weak-looking guy, with wrists about as big as pencils. ...Finally, what he did,
instead of taking back what he said, he jumped out the window. I was in the shower and
all, and even I could hear hm land outside. ...I ran downstairs too, and there was old
James Castle, laying right on the stone steps and all. He was dead, and his teeth, and
blood, were all over the place, and nobody would even go near
him."

On page three there's
an example of attention deficit, when Holden leaves the equipment for the fencing team
on the subway, resuliting in forfeiture of the match.

readability="10">

I was the goddam manager for the fencing team.
Very big deal. We'd gone in to New York that morning for this fencing meet with McBurney
School. Only, we didn't have the meet. I left all the foils and equipemnt and stuff on
the goddam subway. It wasn't all my falult. I had to keep getting up to look at this
map, so we'd know where to get otff. ...The whole team ostracized me the whole way back
on the train.

In Chapter 6
there's an example of weeping: 

readability="8">

"I just lay theere on the floor for a while, and
kept calling him a moron sonuvabitch. I was so mad, I was practicaly
bawling."

Also Chapter 6,
Holden becomes enraged over the prospect of Stradlater "giving the time" to
Jane:

Give
her the time in Ed Banky's goddam car?" My voice was shaking something
awful.

"What a thing to say. Want me to wash your mouth out
with soap?"

"Did you?"

"That's
a professional secret, buddy."

This next part I don't
remember so hot. All I know is I got up from the bed, like I was going down to the can
or something, and then I tried to sock him, with all my might, right smack in the
toothbrush, so it would split his goddam throat open. Only, I missed. ...Anyway, the
next thing I knew I was on the godam floor and he was sitting on my
chest,...

As a post above,
says, Holden is a poster boy for PTSD.