(CNN) — (CNN) --
The judge in the court-martial of an Army psychiatrist charged in a deadly shooting spree on a Texas military base rejected three options presented by his lawyers under which he would plead guilty and ordered the trial to begin in May.
Maj. Nidal Hasan is charged with killing 13 people at Fort Hood in November 2009, called the worst incident of its kind on a military base.
Col. Tara Osborn on Wednesday ruled that pre-trial publicity around the case would not unfairly prejudice a jury and set the start of jury selection for May 29. Testimony is scheduled to begin July 1.
Hasan's lawyers filed motions indicting that he was willing to plead guilty under three scenarios. Details of the proposals were not immediately clear.
But Osborn turned them down, saying it would be tantamount to admitting guilt to a capital offense, which is not permitted under military law.
Hasan, who was paralyzed from the waist down in an exchange of gunfire with police, appeared bearded and thinner when he arrived for the pretrial hearing in a wheelchair.
The attack that resulted in murder and attempted murder charges against him occurred at the post's processing center, where soldiers were preparing to deploy to Afghanistan and Iraq.
Prosecutors aim to show that Hasan was a radical Islamist.
Investigations have found that he had been communicating via e-mail with Anwar al-Awlaki, a prominent radical Yemeni-American cleric killed by a U.S. drone attack in 2011.
And much of Wednesday's hearing was devoted to questioning a potential expert witness for the prosecution, Evan Kohlman, an international terrorism expert who apparently examined the contents of a laptop belonging to Hasan.
Kohlman said he found examples of websites and YouTube videos that could indicate someone trying to learn more about radical Islam. He said there was "no indication that anyone other than Hasan used the laptop."
One item on the laptop that was cited by Kohlman linked to a YouTube video of a 2009 CNN report featuring the network's national security analyst, Peter Bergen, talking about a newly released audio tape from Osama bin Laden.
Defense lawyers, who want to keep Kohlman off the stand at trial and sought to undercut his methodology and conclusions, introduced their own expert witness who said that only a portion of the CNN report had been viewed.
The start of Hasan's court-martial has been repeatedly delayed since it was initially set to begin in March 2012, most notably after an appeals court delayed the case over the question of whether the Army major's beard could be forcibly shaved.
Army regulations prevent soldiers from wearing facial hair while in uniform. Hasan, who is still considered a soldier, is a practicing Muslim and maintains he has the right to wear the beard under U.S. laws protecting religious freedoms.