Apple Inc. Chief Executive Officer Tim Cook was ordered on Thursday to give a deposition in a lawsuit claiming the iPhone maker and other technology companies violated antitrust laws by entering into agreements to not recruit each other’s employees.

U.S. District Judge Lucy Koh in San Jose, California, issued the order at a hearing over the objections of George Riley, a lawyer representing Apple. The other defendants in the case include Google Inc., Intel Corp., Adobe Systems Inc., Walt Disney Co.’s Pixar animation unit, Intuit Inc. and Lucasfilm Ltd.

The lawsuit before Koh is a private lawsuit brought on behalf of employees that mirrors claims the companies settled with the U.S. Justice Department in 2010 following a probe. The case claims the companies agreed to refrain from placing “cold calls” to lure workers from competitors.

Koh told lawyers today that Apple founder Steve Jobs was copied on e-mails at issue in the case, and that she found it “hard to believe” that Cook, as Apple’s chief operating officer at the time in question, wouldn’t have been consulted about such agreements.

The judge said she was disappointed that senior executives at the companies involved hadn’t been deposed before Thursday’s hearing over whether she should certify the case as a group lawsuit. The class would include different categories of employees whose incomes, their lawyers argue, were artificially reduced because of the collusion. Koh didn’t rule on class certification.

Google Chairman

At Koh’s request, the lawyers also agreed that Google Chairman Eric Schmidt will be deposed Feb. 20.

Lawyers for the employees will depose Intel Chief Executive Officer Paul Otellini later this month, lawyers said.

Robert Mittelstaedt, a lawyer representing the companies, argued that the employees’ lawyers haven’t demonstrated that everyone in the proposed class was hurt by any such agreements, as is required for the group to be certified as a class.

“You can’t assume that if someone got a raise from a cold call” that the effect of that negotiation would “ripple to everybody else,” Mittelstaedt told Koh. “Why would a company give a raise to someone in a negotiation if it knew it had to turn around and give a raise to everyone else?”

The proposed class of employees includes engineers, sous chefs, administrative assistants and others, because all of the employees were harmed by the companies’ conduct and will rely on the same evidence to prove their damages, lawyers for the workers said in a court filing.

In the 2010 settlement, the Justice Department said the companies kept do-not-call lists to avoid competitive recruiting, and that such agreements restrained competition, which hurt employees.

Adobe, Apple

The government said that in May 2005, senior Adobe and Apple executives agreed not to cold-call each other’s employees. Adobe was placed on an internal Apple “do-not-call” list, while Adobe put Apple on a list of “companies that are off- limits,” according to the department.

Apple and Google had each other on internal do-not-call lists starting in 2006, according to the department. The next year, Apple and Pixar agreed not to call each other’s staffs, and Google entered into no-cold-calling agreements with Intel and Intuit, the department said.

The San Jose case is In Re High-Tech Employee Antitrust Litigation, 11-2509, U.S. District Court, Northern District of California (San Jose). The previous case is U.S. v. Adobe Systems, 10-cv-1629, U.S. District Court, District of Columbia (Washington).