The 32-year-old gold medal-winner risks a jail sentence, Brazilian media quoted a police official as saying, although the judicial authorities had yet to confirm that.
“Ryan Lochte was charged with the crime of falsely reporting a crime,” police said in a statement, adding that the case had been referred to the courts.
The police statement said they had recommended the courts issue a summons for Lochte to be questioned.
“Once he is summoned, whether he turns up or not, the penalty is the same: one to six months’ prison,” the news website G1 Rio quoted police official Clemente Braune as saying.
“If he is summoned and does not turn up to the hearing, the trial will go ahead in the accused’s absence until the final sentence is given.”
Lochte apologized last week for saying that he and three teammates had been mugged on their way back from an all-night party by robbers pretending to be police.
Rio police chief Fernando Veloso later told a news conference that the swimmers were not robbed but detained when they tried to flee after vandalizing a gas station bathroom.
The tale humiliated first the Brazilian hosts of the Games and later Lochte’s own Team USA after police contested his story.
Top sponsors such as Speedo and Ralph Lauren abandoned Lochte this week.
“I’m taking full responsibility for it,” Lochte said in an interview broadcast late Saturday.
“I over-exaggerated that story and if I had never done that, we wouldn’t be in this mess.”