The battle over documents in the George Washington Bridge lane-closing case continued Tuesday as prosecutors filed papers claiming materials produced by one of the defendants weren't given under immunity and were properly used to bring the indictment last year.

At issue in Tuesday's filing were documents provided by former Port Authority of New York and New Jersey official Bill Baroni to a New Jersey legislative committee investigating the 2013 lane closures near the bridge.

Baroni has claimed in court filings that the documents were given under an immunity agreement but that the federal government violated his Fifth Amendment rights by improperly using the materials to indict him. He is seeking to have the charges against him dismissed.

Baroni and Bridget Kelly, a former deputy chief of staff to Gov. Chris Christie, are scheduled to go on trial in September on wire fraud and civil rights charges. They're alleged to have ordered the access lanes closed to cause traffic jams in Fort Lee to punish the town's mayor for not endorsing Christie for re-election.

Christie has not been charged.

Baroni produced documents to the Select Committee on Investigation in early 2014 accompanied by a cover letter that invoked New Jersey's immunity statute, but the government's brief Tuesday claimed Baroni "ignores that the SCI itself expressly disclaimed immunity in a letter to Baroni's former counsel, dated February 25, 2014."

Baroni also has argued that his testimony to a different state legislative committee in late 2013, in which he said the lane closures were part of a traffic study by the Port Authority, was given under immunity and should not have been used to bring the federal indictment.

The prosecution of Baroni and Kelly has generated hundreds of thousands of pages of documents, some of which are still in dispute.

The defendants have sought interview notes from the 2014 report by Gibson, Dunn and Crutcher, the taxpayer-funded law firm Christie hired (and which exonerated him of wrongdoing), as well as documents Christie's office has kept confidential by invoking privilege rules.

The law firm has a Thursday deadline to comply with a subpoena filed by Kelly and Baroni that seeks those documents, which include communications between Christie's office and the Port Authority, which operates the bridge.

New Jersey taxpayers had been billed more than $10 million for the law firm's work on behalf of Christie's office in the case, according to figures released in February.

Baroni and Kelly also are seeking a list of people the U.S. attorney's office has indicated may have known about the lane-closing but weren't involved in the alleged conspiracy.

News organizations including The Associated Press have gone to court to try and get a list of people prosecutors believe were involved but weren't charged. The government has opposed the request, and a judge has yet to rule on the matter.