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Local broadcaster WLKY reported on Thursday that LMPD Chief Erika Shields revealed that the FBI had begun investigating the officers.
She said she does not have specifics on the incident as it occurred prior to her taking over the department.
Ms Shields said she was given very little information from the FBI, but suggested things were not looking good for the police department.
"My sense is it will be another black eye to the department and is going to show some very poor judgment by a select few individuals on this department," she said.
Ms Shields said the officers at the centre of the investigation have not been suspended, but were put on "desk duty" until the investigation finishes.
The chief suggested that a video of the attack exists, but said she has not seen it.
"That is absolutely sickening and disgusting and I hope that nobody makes excuses for that kind of behavior and I hope that's the kind of thing that is dealt with with the kind of swiftness and seriousness that the behavior justifies," Councilwoman Jessica Green said.
Timothy Beam, a spokesman for the Louisville FBI office, told the Courier Journal that the agency was "investigating whether these incidents violated federal law," but said he "cannot" comment on the specifics of the investigation.
Police officers in Los Angeles came under fire last month after a high-profile clearing out of Echo Park of its sizable homeless population.
Activists protested the city's decision to wall off the park and drive out the more than 200 homeless individuals camping inside the park.
Those defending the homeless population said the group had formed a community where people could help each other and find some semblance of stability living at the park.
However, the city's Mayor Eric Garcetti told broadcaster KTLA on 26 March that the park was becoming increasingly dangerous.
"Four people died in this park. Things continue to grow. Women are being abused, sexually exploited."
City and county officials gave the homeless people living at the camp the option of being moved to shelters or residents through Project Roomkey, which housed people during the pandemic. Some took the city up on the offer, while others chose to stay on the streets.