She went "down the chute and slid down like garbage," the man told the Daily News.
The newspaper reported that the victim’s purse was found near the building’s elevator.
Residents told CBS New York they got an email from building management telling them not to use the trash chute, but were not told much about what was going on.
"It's scary," resident Nicki Leitner told the news station. "In fact, when I texted my boyfriend about this, he told me to get out of the building because he was worried, as was I. But it was so hush-hush."
Zeckendorf Towers, which is comprised of four 29-story towers, is located a block from Union Square Park. According to CityRealty.com, the towers house 630 apartments.
The building has a man on the door 24 hours per day, the website said. A one-bedroom condo was listed at an average sale price of $1.2 million.
CBS New York reported that the building has been home to high-profile residents, including disgraced former U.S. Rep. Anthony Weiner and his estranged wife, Democratic political advisor Huma Abedin.