COLOMBO Capo John Pate told shrinks his dead grandmother urged him to commit suicide, and it was felt in some quarters that possibly the man was too nuts to be much of a prosecution witness.

Indeed, a district judge had decided that Pate was too mentally unfit even for regular prison, ruling that he should spend 15 years in a squirrel cage instead.

But prosecutors insisted that no, Pate (right) had been faking, he was perfectly sane. And they needed him, they said, to help snag a big mob trophy -- Alphonse (Allie) Persico, (left) son of imprisoned-for-life Colombo boss Carmine (Junior) Persico. Alphonse, they charged, had taken part in the bloody Colombo family war in which 10 people died, and Pate could help them prove it.

The younger Persico's murder and racketeering trial ended yesterday -- and if the feds thought that Pate's testimony was going to cement their case against Alphonse, they were dead wrong.

"Pate did everything he could to help Allie," lamented one top federal official. "But not enough that we can do anything about it," he grunted.

Pate did link Alphonse to the killing of his brother-in-law, Steve Piazza, but he failed to implicate him in any of the war crimes, any of the four Persico faction killings in 1991 and 1992.

He testified, for example, that months before the shooting war started, he visited Alphonse in federal prison to thank him for getting three Persico capos to attend a peace meeting between the opposing factions.

He also insisted that Persico had no idea that Pate had used part of a $250,000 stake that Persico had given him before going to prison to buy guns, ammunition and bulletproof vests for the war effort.

"He had no knowledge," said Pate. "As far as I know, he had none of that information from me."

Pate was the only witness to provide firsthand evidence about Persico's alleged role in the war, and his testimony was key to the case.

As Allie walked free out of court yesterday, prosecutors may well have agreed that Pate really is crazy.

Like a fox.