There is no such document in existence. There is a limestone block recording the dedication of a building to the memory of Augustus which mentions Pontius Pilate as Prefect of Judea, and this is the only record of his existence.

However, depending on who you talk to, there is arguably no non-biblical contemporary record of Jesus whatsoever. A frequently cited reference can be found in the work of Josephus, a 1st Century Jewish Historian who wrote extensively on the Jewish Revolt. While his work does mention Jesus briefly in several instances, evidence suggests that at least part of these passages are a forgery, inserted centuries later by Christian apologists.

It is important to note, however, that plenty of biblical scholars believe that these forgeries conceal a kernel of truth, and that they represent an exaggeration of some small mention of Jesus which Josephus actually recorded.

Regardless, no there is no signed execution order.

EDIT: Pilate also receives a minor billing by Philo Judeaus of Alexandria and an even smaller one by Tacitus in the early 2nd century