The lawsuit asked a federal judge to stop Mr. McCulloch from enforcing Missouri laws that restrict what a grand juror can say about the secretive hearings.

The grand jury that considered charges against Mr. Wilson was abnormal both in the scope of the evidence it heard and the time for which it met. In Monday’s lawsuit, the plaintiff said it viewed the Ferguson case as having “a stronger focus on the victim” than other cases the panel considered.

The 12 grand jurors heard evidence on Mr. Brown’s death for months, including testimony from Mr. Wilson and several witnesses. Prosecutors did not seek a specific charge and instead gave grand jurors a list of possible charges to consider. The grand juror who is suing said in the lawsuit that the presentation of possible charges was “made in a muddled and untimely manner” compared with other cases that jurors had heard.

Mr. Brown’s death set off months of protests in and around Ferguson about race and how police use lethal force. When Mr. McCulloch announced in November that the grand jury had not indicted Mr. Wilson, protests increased in intensity. Though most demonstrations were peaceful, two violent nights in the Ferguson area resulted in several businesses being looted and police cars being burned.