The teen died along with Metro Madrid maintenance manager José Manuel when the train crashed into a berm at the end of a test track on August 7, 2013.
"At the moment of the accident she was behind the controls of the train," the report of an investigating judge said, according to an online report from 20 Minutes newspaper, which said it obtained the document.
The au pair worked for the family of 36-year-old Manuel, who offered to let her drive the train, the newspaper said.
Manuel was giving her, his wife and his four-year-old son a tour of a shed where Metro Madrid trains were stored when the accident occurred.
Manuel's wife and son received minor injuries in the crash.
The maintenance manager was sufficiently qualified to drive the subway trains, 20 Minutes said.
However, he did not notify colleagues of his intention to drive one on that particular day, the newspaper said.
"The prosecutor has decided to shelve the case, because even if he found alleged person responsible for the tragedy, he is dead,” a Madrid court spokesman is quoted as saying.
The family of the au pair girl has declined to comment on the conclusions of the report, The Local Switzerland reported.