Brancheau was killed two weeks ago after being thrashed underwater before a horrified audience. SeaWorld's cameras recorded the death, and the tapes were voluntarily turned over to law enforcement.
Once the Orange County Sheriff's Office concludes its investigation, the material would become public under Florida law.
Brancheau's family said Monday through a spokesman that public airing of the killing would only worsen their grief.
"Use of this video will do nothing more than further sensationalize a tragic event and traumatize our family," spokesman Charles LoVerde said to the Orlando Sentinel. "Our family has a right to heal in private, and we once again appeal to the media to recognize the terrible pain we are experiencing and give us a small measure of respect and privacy."
They could seek a court injunction to stop the release, at least temporarily.
The family has been consulting the lawyer who represented Dale Earnhardt's widow in an eventually successful court fight over his autopsy photos.
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February 24, 2010 - SeaWorld Trainer Killed by Tillikum the Whale