"Time for some traffic problems in Fort Lee," she wrote in an August e-mail to David Wildstein, a former official at the Port Authority of New York and New Jersey, which operates the bridge.
Documents show Stepien in communication with other key players and mocking the mayor.
Christie has denied any involvement in a plot to create gridlock.
Assemblyman John S. Wisniewski (D., Middlesex) and Sen. Loretta Weinberg (D., Bergen), cochairs of the committee, said in a statement: "Today's court filings are an unfortunate but necessary step to further the committee's work. The committee remains confident in its legal position. We will now let the judicial process play out."
Lawyers for Stepien and Kelly said early Wednesday evening that they had not yet reviewed the filings.
The court briefs say Kelly and Stepien could invoke the Fifth Amendment only if they faced a "substantial and real hazard of incrimination."
While the former aides note that the U.S. Attorney's Office is conducting a parallel criminal investigation, the committee said in the filings Wednesday that they had provided no evidence that they are targets of the investigation "at this time."
In a Jan. 31 letter to the lawyer for the committee, Stepien's lawyer, Kevin Marino, pointed to remarks by Wisniewski during an appearance on CNN that "laws have been broken" in connection with the lane closures.
In a filing addressing Stepien, the committee said it had no authority to initiate a criminal prosecution. Wisniewski's comments reflected "the preliminary views of one of 12 committee members" and did not refer specifically to Stepien, the committee said.
Stepien and Kelly had argued that providing documents could lead to their being incriminated, in violation of the Fifth Amendment's protections.
The committee said the documents it requested - related to the lane closures - were not necessarily incriminating. The committee also disagreed with Stepien and Kelly about whether the act of responding to a subpoena was protected by the Fifth Amendment, which generally applies to testimony.
Stepien and Kelly previously argued that responding to the committee would require that they decide which documents were relevant to the probe, similar to giving testimony.
Such an interpretation, however, "would effectively end all investigative activity, legislative or otherwise, regardless of whether it dealt with a potential abuse of power or something even more severe, such as a potential attack against the United States," the committee said.
Michael Critchley, Kelly's attorney, said Wednesday that Kelly had not changed her position.
"We are going to stand on that [Fifth Amendment] privilege until and unless the court tells us that position" is not valid, he said.
The committee also said its subpoenas were tailored narrowly to the Sept. 9-13 reduction of access to the bridge.
Nor do the subpoenas violate the Fourth Amendment, the court briefs say, arguing that the Supreme Court "has consistently upheld broad legislative and administrative subpoena requests pursuant to equally broad legislative investigations when faced with" such challenges to the requests.
Lawmakers have issued nearly 40 subpoenas in the probe of the lane closures and are waiting for documents from numerous recipients.
Only Kelly and Stepien have declined to comply with the document requests, Wisniewski said.