David Lee Turner was shot and killed in July after allegedly hitting a deputy with a bag of beer. Authorities had been investigating a report that minors asked adults to buy alcohol in the area.
Security video shows Turner walking out of a liquor store with the beer, but the tape stops before the deadly altercation.
Turner's family says the tape has been edited.
"It's only obvious. I mean, you see one thing on one view, and then it stops and skips," said Turner's sister Ernestine Martin.
An attorney for Turner's family said the shooting was indeed videotaped. A deputy stated in a search warrant that he viewed "the entire incident" on tape. A sheriff's spokesman says the warrant wording meant the incident was captured but not every detail.
Sheriff's officials determined the shooting was within department policy.
Turner played for the Cincinnati Bengals from 1978 to 1980.
The Associated Press contributed to this report.