When the Staten Island district attorney called for a special prosecutor to investigate one of New York City’s political parties, he went to unusual lengths to keep his motivations secret, seeking special permission to file his request under seal.

Now the leaders of the Working Families Party, the subject of the investigation, are asking a state judge to unseal the case and penalize the district attorney, Daniel M. Donovan Jr., for undermining his own request for secrecy by leaking portions of documents that were blocked from public release to the news media, according to a legal complaint filed on Wednesday.

It was another odd development in a long-running case, about which little is known but which has fueled a feud between Mr. Donovan, a Republican, and the Working Families Party.