Setting up a likely court battle, two former aides to Gov. Chris Christie of New Jersey refused again on Tuesday to provide materials subpoenaed by the legislative panel investigating the politically charged lane closings leading to the George Washington Bridge last September.

The special investigative committee had sought information and devices, like cellphones from Bill Stepien, Mr. Christie’s two-time campaign manager, and Bridget Anne Kelly, a former deputy chief of staff to the governor. Ms. Kelly sent an email in August calling for “some traffic problems in Fort Lee,” the town at one end of the bridge whose mayor did not endorse Mr. Christie for re-election.

After lawyers for the two refused to turn over information earlier this month, citing privacy as well as the constitutional right against self-incrimination, the legislative panel voted to allow its special counsel to take whatever measures he believed necessary to compel them to comply.

The counsel, Reid Schar, tried to open a discussion about conditions under which the lawyers might turn over at least some information, offering a new deadline to meet the demands of the subpoena, and to view the materials privately.