RIO DE JANEIRO — The Brazilian police recommended on Thursday that prosecutors file charges against Ryan Lochte, the American Olympic swimmer, for the crime of providing false testimony, an indication that while the Summer Games here have ended, his misadventure in Brazil may continue.

As of Thursday evening, the state prosecutor’s office had yet to receive the police recommendation. Prosecutors are the authorities who would file formal charges against Mr. Lochte, a gold medalist.

The state prosecutor’s office “will analyze the police recommendation and either file charges with the judiciary or not take further action,” said a spokeswoman at that office, who was not authorized to speak on the record, on Thursday evening.

In other words, Mr. Lochte “is still not a defendant,” according to a spokesman with the Rio de Janeiro state judiciary, who also was not authorized to speak on the record.