Volkswagen pleaded guilty in January to criminal charges in the United States related to the emissions cheating, but the prosecution of individuals is just beginning. Mr. Schmidt is one of six current of former Volkswagen employees indicted in the United States, and the only one in custody; the others are in Germany. He is the first of nearly 37 people under investigation in Germany to give his side of the story in court documents.

Federal prosecutors in the United States have accused Mr. Schmidt, a 48-year-old German, of knowingly providing false information to American regulators after they became suspicious about the emissions of Volkswagen diesel vehicles in early 2014.

The campaign of obfuscation and delay continued until September 2015, the indictment says, when Volkswagen confessed that engine computers in its diesel cars had been programmed to cover up emissions that were worse than those of long-haul trucks.

Mr. Schmidt details a much different version of events in documents filed by his lawyers in a bid to persuade a judge to release him from a federal detention center in Detroit. Mr. Schmidt has been held without bail since January, when he was arrested in Miami after spending Christmas with friends in the United States.

Mr. Schmidt’s legal motion does not dispute that he acted as Volkswagen’s liaison with regulators from the Environmental Protection Agency and the California Air Resources Board, the state agency known as C.A.R.B. that took the lead in exposing the emissions cheating. Alberto Ayala, deputy executive officer of C.A.R.B., said in an interview last year that Mr. Schmidt had presented him with binders filled with bogus technical information to try to keep the agency from discovering the fraud.