Interesting question. In a search on "death of Pilate" I found a (big C) Catholic online encyclopedia with the following:

Then the emperor ordered him to be kept in prison, until he should deliberate in a council of the wise men what ought to be done with him. And a few days after, sentence was therefore passed upon Pilate, that he should be condemned to the most disgraceful death. Pilate, hearing this, killed himself with his own knife, and by such a death ended his life.

When Caesar knew of the death of Pilate, he said: Truly he has died by a most disgraceful death, whom his own hand has not spared. He is therefore bound to a great mass, and sunk into the river Tiber. But malignant and filthy spirits in his malignant and filthy body, all rejoicing together, kept moving themselves in the waters, and in a terrible manner brought lightnings and tempests, thunders and hail-storms, in the air, so that all men were kept in horrible fear. Wherefore the Romans, drawing him out of the river Tiber, in derision carried him down to Vienna, and sunk him in the river Rhone. For Vienna is called, as it were, Via Gehennoe, the way of Gehenna, because it was then a place of cursing. But there evil spirits were present, working the same things in the same place. Those men therefore, not enduring such a visitation of demons, removed froth themselves that vessel of malediction, and sent him to be buried in the territory of Losania. And they, seeing that they were troubled by the aforesaid visitations, removed him from themselves, and sunk him in a certain pit surrounded by mountains, where to this day, according to the account of some, certain diabolical machinations are said to bubble up.

This passage, along with a description of Pilate wearing Christ's garment in front of Caesar and realizing some beneficial effect, occured several places in my search. An interesting site that posts this same description then argues against it can be found here. It is part of a larger blended philosophy webring. Really interesting stuff, when you start poking around. (This is the table of contents--and makes this philosopher's heart race just to see all of the great topics!)

SRS