(CNN) -- The State Attorney's Office in Florida is investigating an incident in which a person identified as a police lieutenant's son is shown on videotape punching a man described as homeless, authorities said.
A police report said the incident took place early on December 4. But Justin Collison, the son of a Sanford, Florida, police lieutenant, has not been arrested or charged, CNN affiliate WFTV reported Tuesday.
However, Sanford Police Chief Brian Tooley told CNN on Thursday that authorities obtained an arrest warrant for Collison on Wednesday night on suspicion of aggravated battery, and that "officers are out looking for him."
"I'm hoping he'll come and turn himself in," Tooley said. "But we'll apprehend him."
WFTV aired video of the fight, in which the person identified as Collison is seen punching the man -- who apparently was attempting to break up an unrelated fight outside a bar -- in the back of the head. The man appeared to be unconscious for at least several minutes after the blow, according to the video.
Sanford police had said that Collison, 21, was not being given preferential treatment. Tooley acknowledged Thursday, however, that "there's a lot of things that could have been done better," and said an internal investigation is under way.
Repeated attempts by CNN to contact Collison and his father were unsuccessful Thursday.
On the tape, the person identified as Collison strikes the man in the back of the head, then walks a short distance and pushes a second man, throwing him to the ground as others shout for "Justin" to stop. The second man left the scene before police arrived, according to the police report.
"I was like, 'God, this guy, he's got to go to jail,'" the man who filmed the incident told WFTV. He did not want to be identified. "You can't walk around doing that kind of stuff."
The first man, identified in the police report as Sherman L. Ware, was described by others on the video as homeless. He fell forward upon being struck and hit his face on a pole, according to the police report. Ware was treated at a hospital for a broken nose, but the police report described him as intoxicated and uncooperative, saying he did not want to provide a sworn statement. In addition, witness accounts of the incident were conflicting, the report said.
Tooley said officers did obtain a statement from Ware on Wednesday night.
Tooley said once the responding officers realized a lieutenant's son was involved, the captain on duty should have been called, and Tooley said he should have been notified as well.
"What should have made a difference, in my opinion, is that this was in fact the son of a lieutenant," he said. "They should have made sure they did everything exactly by the book."
Authorities have asked the State Attorney's Office for Brevard and Seminole counties to review the incident and assess whether charges should be filed. "This case will be forwarded to the SAO for further evaluation for investigation and prosecution," the police report says.
The investigation is under way, Lynne Bumpus-Hooper, spokeswoman for the state attorney's office, said Thursday. The length of the investigation is "well within the realm of normal," she added, saying such probes can take anywhere from two weeks to three months. The speed of the investigation has much to do with a public safety threat, she said; if someone is a threat, the investigation will be rushed.
An interview between the prosecutor and the victim is scheduled to take place next week, she said, and no decision on charges will be made until after that interview takes place. "Part of the issue we face is evaluating the degree of damage, harm to the victim, because that determines the charge filed," Bumpus-Hooper said.
Prosecutors said they also intend to subpoena medical records and hope to get the victim's consent to obtain them, which speeds the process. "There is a lot of information we need," Bumpus-Hooper said.
Tooley said he spoke to the state attorney and the chief assistant state attorney on Wednesday and "they agreed to expedite this process."
He said he was not aware of the incident -- and the fact it involved a lieutenant's son -- until four days after it happened. He said he saw the video for the first time on television news.
"I completely understand the public's frustration, outrage," he said. "It's a shocking video ... I wish I would have seen the video two or three weeks earlier."
Responding officers arriving at a barroom brawl incident are frequently unable to sort out what happened, and call in the State Attorney's Office to investigate, Bumpus-Hooper said. Police requested the incident be investigated as an aggravated battery, she noted, a serious charge.
Whether a person is a law enforcement officer's relative "makes absolutely no difference to this office," said Bumpus-Hooper. She said the office has investigated relatives of police officers before and currently has cases pending against law enforcement officers.
On whether the video will help the investigation, Bumpus-Hooper said she hasn't asked the state's attorney, but "generally the more evidence you have, the better off you are." She said authorities would also be interested in knowing what happened before the tape started and what took place inside the club.
Tooley said the incident has not affected Collison's father's employment status.
CNN's Anna Rhett Miller contributed to this report.