Central Electoral Commission President Roberto Rosario said at a press conference that Nunez signed a sworn statement saying he is not the person identified in official documents.
Dominican authorities also have arrested Hector Pena Diaz, who is accused of falsifying Nunez's documents.
Nunez returned to his native Dominican Republic on Thursday amid accusations that he was playing under an assumed name.
A person familiar with Nunez's immigration status told The Associated Press on Thursday that his real name is Juan Carlos Oviedo, and he's 29, a year older than listed in the team media guide.
The person also said the Marlins have been aware of the issue for several months. The person spoke to the AP on condition of anonymity because team officials haven't made any official statements on the case.
His quick departure left his former team searching for answers.
"It's the first time I had a, how should I say this, a guy playing with an alias," manager Jack McKeon said before Florida played the Milwaukee Brewers on Friday night. "I don't know what the circumstances are."
The Marlins placed Nunez on Major League Baseball's restricted list, and he isn't expected to pitch in the final week of the season. He had 36 saves and a 4.06 ERA in 68 games.
Reliever Edward Mujica said he spoke with Nunez almost daily, but never sensed any problems brewing.
"I talked to him on Wednesday in the bullpen," Mujica said. "He didn't say nothing to me."
Mujica said the only possible hint of something being wrong happened in August when the Marlins played at Colorado.
"He told me he had some problems with his family," Mujica said, but added that Nunez didn't elaborate.
Nunez, who is married, was born in Jamao al Norte, Dominican Republic, and lives in Bonao, according to his Marlins biography.
He turned pro in 2000 after signing with the Pittsburgh Pirates. Nunez was traded to Kansas City in late 2004 and made his major league debut with the Royals the next season. The Marlins traded for him after the 2008 season.