The First Department determined a writ of prohibition could not be employed by Brazilian citizens to stop a prosecution by the district attorney.  Petitioners had other legal remedies including pretrial motions and appeal if convicted.  The fact that petitioners would have to defend the prosecution in New York to use the alternative remedies did not render those remedies inadequate:

In this action for a writ of prohibition directing the DA to stay the prosecution of petitioners, Brazilian citizens (the former mayor of Sao Paolo and his son) who have been indicted in New York for crimes relating to the theft of more than $11 million in Brazilian public funds that were allegedly transferred to petitioners’ account in a bank located in New York, the petition was properly denied. The extraordinary remedy of prohibition is not available to petitioners, who assert that the underlying criminal action violates their statutory and constitutional rights to a speedy trial and their right to due process, or, in the alternative, that the indictment should be dismissed either in furtherance of justice pursuant to CPL 210.40(1) or under principles of international comity. These claims allege errors of law for which petitioners have adequate alternative remedies, including filing pretrial motions in the underlying criminal action and challenging any conviction on appeal … . That petitioners would have to voluntarily leave their home country to appear for arraignment since Brazil will not extradite its own citizens before availing themselves of such remedies does not render them inadequate … . Matter of Naluf v Vance, 2014 NY Slip Op 02546, 1st Dept 4-15-14