The "Goodfellas" star gave his account of the Jan. 22 incident last week at a Boca Raton home where he was staying, police spokesman Sgt. Jeff Kelly said. Garry Serino, who was with Pesci at the time, also gave police a statement.
Kelly did not provide details because of the investigation.
"There are two sides to every story," Kelly said.
Police were preparing to send the investigation results to the Palm Beach County prosecutors to determine whether Pesci should be charged with misdemeanor battery for allegedly punching Juan Carlos Montenegro, 24.
Montenegro, a Broward Community College student, told police that after encountering Pesci, 62, he shook the actor's hand and told him he was a big fan. He then purchased a camera, walked toward Pesci and asked for a picture, but the actor refused, he said.
Montenegro kept asking to take a picture, and when Pesci turned, Montenegro took the photograph. Pesci then punched him with his right fist, the report said.
If Pesci is charged, he would be issued a court summons, and would not be booked into the county jail, said Mike Edmondson, state attorney's office spokesman.
Pesci's attorney, Jay Julien, did not return a call for comment.