James, whose complaint of mistreatment of his son led to Leach's firing, declined to comment as he walked into the university's administration building before his deposition.
Leach gave more than five hours of sworn testimony Friday. When asked if he would be questioning James, he said, "I'm not allowed to."
Adam James, the son of the ESPN analyst and former NFL player, also testified under oath later Saturday. Leach was not in the room when the younger James gives his deposition. Father and son each gave about four hours of testimony.
The university fired Leach Dec. 30, two days after suspending him amid allegations he mistreated Adam James, who had a concussion. Adam James contends his coach twice ordered him to stand for hours while confined in a dark place during practice.
Leach has denied mistreating the receiver and suspects an $800,000 bonus he was to have received Dec. 31 was the reason he was fired. His lawsuit includes allegations of libel and slander and breach of contract. Leach had just completed the first year of a five-year, $12.7 milliion deal that came after months of negotiations.
An attorney for Texas Tech, Dicky Grigg, told reporters Saturday that Craig James testified that initiallly he only wanted Leach to accept responsibility for the alleged mistreatment of his son.
Grigg also said that Leach didn't believe the receiver had a concussion and that he "pressured" a trainer "to make Adam practice." That's what led James to seek Leach's dismissal, Grigg said.
"He made no bones about it," he said of James wanting Leach fired.
Ted Liggett, one of Leach's attorneys, said there is no "evidence or facts" to those claims. Leach treated Adam James "as if he had a concussion from the moment he discovered had a concussion. So we categorically deny that."
Liggett said Adam James testified that he thought being placed in the shed on Dec. 17 "was funny."
The younger James also testified that he "felt no threat of physical harm, and he didn't think that a coach should be fired for the incident that took place on Dec. 17," Liggett said.
Another of Leach's lawyers, Paul Dobrowski, said Friday that depositions from Texas Tech chancellor Kent Hance and a school attorney bolstered the former coach's contention that he didn't mistreat Adam James and that Leach had a right to sue the school "without fear of retribution."
Grigg said Friday that the university was "very pleased" with the depositions given by Hance and a school attorney who conducted the investigation into the allegations against Leach.