California police say Hilton is being investigated for petty theft after allegedly taking a copy of the video from a newsstand without paying for it.
The TV show Celebrity Justice has posted a video on its Web site that shows Hilton buying several magazines. It goes on to show Hilton becoming enraged when she spotted the video.
Gerry Castro, an employee at Swing News in West Hollywood, told Celebrity Justice that Hilton became enraged after spotting the sex video "One Night in Paris" on sale at the newsstand.
"She threw her 80 cents change at me and took the video and said, 'I'm taking this and I'm not buying it,'" Castro told the show.
The sex tape surfaced in 2003 just before the start of Hilton's TV series "The Simple Life." She has said she was embarrassed and humiliated that the tape ever became public.
Los Angeles prosecutors say deputies will present the charges early next week and then a decision will be made on whether charges should be filed.
"There was an incident, and she is alleged to have taken something," sheriff's Deputy Steve Suzuki said without disclosing further details.
Calls to Hilton's publicist, Gina Hoffman, were not immediately returned.
Deputies were expected to present the misdemeanor case next week to prosecutors, who will then decide whether to file any charges, said Jane Robison, a spokeswoman for the Los Angeles County district attorney's office.