In the footage, the Olympic medalist can be heard arguing with officers after her big day of drinking at the fun park.
According to the Sentinel, Morgan said: "Dude, you guys are lying right now, I can't imagine what black people go through".
In response to the video's release, Morgan said the video supported her position that she wasn't "highly impared".
Morgan tweeted an apology three days after the incident occurred, stating she will "learn from this (and) make sure it does not happen again".
The 30-minute video depicts Morgan repeatedly asking why she and her friends were taken to private room.
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It involves having a drink at each of the 11 countries in Epcot's World.
"I paid $107 per person, how is that trespassing?"
"They were all being very loud and belligerent toward staff around guests".
Later in the video, one of the two women in the room says: "I'm so glad I'm white".
Initial reports of the incident stated that Morgan told police she "knew the SWAT team", which was believed to be an attempt to coerce police into letting her leave.