Kennedy, 54, a member of the politically powerful Kennedy clan that included her late father, former U.S. Attorney General Robert Kennedy, and late uncle, President John F. Kennedy, is charged with a single count of driving while ability impaired by drugs.
Kennedy was charged after a July 2012 incident in which authorities say she drove down an interstate after taking the sleep-assisting drug Ambien.
The six-member jury deliberated less than an hour after getting the case and will return to its work Friday, the (White Plains) Journal News reported.
The newspaper said the jurors asked Judge Robert Neary for readbacks of some testimony before calling it a day.
During closing arguments, prosecutor Doreen Lloyd urged the jury not to let Kennedy's family ties sway its decision and tried to use the title of Kennedy's own 2000 book, "Speak Truth to Power," to make that point.
"On any given day, anybody could engage in conduct that could be a crime," Lloyd said. "She should be held accountable."
A guilty verdict would "speak truth to power," she said.
Defense attorney Gerald Lefcourt called the prosecution's case "nonsense," the Journal News said. He told the panel there was no proof Kennedy drove while knowing she had taken the sleep-inducing drug.
"That's what they're saying, that she figured it all out, and she drove anyhow," Lefcourt said. "It's just nonsense."