Kennedy, 54, daughter for former U.S. Senator Robert Kennedy and the ex-wife of New York Gov. Andrew Cuomo, testified she did not intentionally take the prescription sleep aid Ambien on the morning of her July 2013 accident.
She is accused of driving under the influence of drugs in the incident in which her car struck the back of a truck.
Prosecutor Doreen Lloyd tried to portray Kennedy as a frequent Ambien user who should have known the drug's effects, but Kennedy responded she never thinks about how the pill affects her before she goes to bed.
"Ambien overtook you without warning?" Lloyd asked.
"Yes," Kennedy replied.
Within minutes of beginning her testimony, Kennedy mentioned her late father, ABC News reported, adding her defense team has used her famous lineage as a focal point in attempting to present her as an upstanding citizen with no drug or alcohol issues.
Kennedy faces up to a year in jail if convicted, but has no prior arrests.
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