The police decision will be sent to prosecutors on Tuesday, which will have 15 days to evaluate the case, a spokeswoman for the attorney general’s office told AFP.
A final decision on the case will be made by a judge.
Neymar has vehemently denied allegations he raped a Brazilian woman in a Paris hotel in May.
The ugly affair, which has dominated headlines and conversations in the soccer-mad country for months, overshadowed Brazil’s preparations for the Copa America.
Hosts Brazil went on to win South America’s showcase tournament without their star player, who was injured in a friendly before the opening match.