The complaint was filed on Friday at a police precinct in San Juan, Puerto Rico, police spokesman Edward Ramírez told The Associated Press on Saturday.
Information including who filed the complaint and details of the allegations are not public, given the nature of the complaint.
A person who was not authorised to speak about the case confirmed that Martin's nephew, Dennis Yadiel Sánchez Martin, filed the complaint.
The person said the complaint does not automatically trigger an arrest because the alleged incident is not recent, adding that police will investigate and determine whether charges are warranted.
Sánchez previously requested a restraining order against Martin in July, but a judge later archived the case after Sánchez admitted under oath that he had never been sexually assaulted by the singer.
Flavia Fernández, a spokeswoman for Martin, told the AP that his legal team is evaluating the situation and not issuing public comment for now.
On Thursday, the artist's lawyers filed a lawsuit against his nephew, whom they described as "troubled". They accused him of extortion, malicious persecution, abuse of law and damages.
They said Sánchez's allegations cost Martin at least $US10 million ($A15 million) worth of cancelled contracts and projects, plus another $US20 million ($A29 million) in damages to his reputation.
The lawsuit states that Sánchez would send up to 10 messages a day to Martin, the majority "meaningless diatribes without any particular purpose". It also accuses him of publishing Martin's private number, forcing him to change it.
In addition, the lawsuit said Sánchez falsely claimed he had a romantic relationship with Martin for seven months and that the singer didn't want it to end and would call Sánchez with frequency.
"Nothing further from the truth," the lawsuit stated.
Lawyers also noted that a judge previously issued Sánchez two restraining orders in an unrelated stalking case.
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