According to the police statement, the court issues a summons for the Olympic swimmer.
The US State Department said it was aware of the request.
Ryan Lochte flew out of Brazil after the Games before he could be questioned about the alleged false claim.
The swimmer initially claimed that he and three fellow athletes were robbed at gunpoint in a taxi by men with a police badge as they returned to the Olympic village from a party.
However, the police say Ryan Lochte made up the story and officers produced video evidence that the group were actually challenged by security guards after they had vandalized a gas station toilet.
Ryan Lochte, 32, has admitted he was drunk and apologized, but he now has to decide whether or not to return to Brazil to defend the charges.
The crime faces a maximum penalty of 18 months in prison and the swimmer can be tried in his absence.
However, it is understood that if Ryan Lochte did attend the hearing he could agree to pay a fine like fellow swimmer Jimmy Feigen, who was with him during the incident.
Jimmy Feigen agreed to donate nearly $11,000 to a Brazilian charity to resolve the case.
The US and Brazil have an extradition treaty which Brazil has flouted in the past. US authorities could take the same stance if Ryan Lochte is found guilty.
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