Lawyers for the two aides dismissed by Gov. Chris Christie of New Jersey in the scandal over the closing of lanes leading to the George Washington Bridge struck back on Friday at the legislative committee investigating the closings, arguing in court filings that if the panel wanted them to turn over documents, it would have to grant the aides broad immunity against prosecution.

A judge will now have to decide whether to force the two aides — Bridget Kelly, a former deputy chief of staff to Mr. Christie, and Bill Stepien, his two-time campaign manager — to comply with a subpoena from the committee.

The legislative committee, formed in January to investigate the lane closings that effectively shut down the borough of Fort Lee for four days last September, has issued 38 subpoenas seeking more information about the role of Mr. Christie’s office, his campaign and the Port Authority of New York and New Jersey, which controls the bridge.

Ms. Kelly and Mr. Stepien are the only two people who have refused to comply, citing their Fifth Amendment right against self-incrimination.