In court documents made available Tuesday, prosecutors argue that Kennedy's case should move forward as it would for other first-time offenders.
Lawyers for Kennedy, 53, had argued in a motion filed in North Castle Town Court last month that she had accidently taken a sleeping pill on July 13, 2012, before she swerved into a tractor-trailer on a highway and was arrested.
But prosecutors argue that a trial should be held to determine whether Kennedy accidentally took the pill.
A lawyer for Kennedy says he'll respond to the motion this month.
Kennedy, the daughter of the late Sen. Robert F. Kennedy, was arrested after the car she hit the tractor trailer and frightened other motorists as she drove erratically south on Interstate 684 about 8 a.m. She left the highway at Exit 3, and a North Castle police officer found her slumped over the steering wheel of her 2008 Lexus on nearby Route 22, authorities said.
"I remember getting on the highway, and then I have no memory until I was stopped at a traffic light and a police officer was at my car door," Kennedy told reporters after her first appearance in North Castle Town Court. "In my discussion with the police officer, I was confused and erratic."
Kennedy, who was alone and headed to the gym when the incident occurred, said she "told the officer that it was theoretically possible that I had mistakenly taken an Ambien rather than a thyroid pill earlier that morning."
Kennedy, who lives in Bedford, initially blamed the incident on a partial seizure that was caused by a previously undiagnosed condition. State Police blood tests taken July 13, however, showed that Kennedy had the prescription sleep aid in her system.