The poll published by O Globo newspaper a month before the opening ceremony on August 5 found that 85 percent of city residents see violent crime as a threat to the success of the first Olympics held in South America.
The next biggest threat cited, at 39 percent, was inadequate transport.
Health fears such as the mosquito-carried Zika virus came at the bottom of the list, with only 17 percent thinking this poses a serious threat to the Games.
Some athletes, notably golf players, have cancelled participation in the Olympics because of Zika fears.
Despite a rise in crime in Rio over the last few months and a budget crisis afflicting the police and public hospitals, the poll found that 61 percent of locals still think the Olympics will be a success. However, 27 percent foresee a failure.
The poll was carried out by Sesc RJ, a non-profit that promotes culture, and by the research group FGV Projetos.