The North Castle judge is expected to rule Tuesday on Kennedy's motion to dismiss the charge.
Kennedy is the daughter of the late Sen. Robert F. Kennedy and the ex-wife of Gov. Andrew Cuomo. She was arrested in July after her Lexus swerved into a tractor-trailer near her home north of New York City.
Police said she failed sobriety tests.
A small amount of a sleeping drug was found in Kennedy's blood. She said she believes she accidentally took a sleeping pill that morning instead of thyroid medication.
The defense says fairness demands a dismissal. But prosecutors say dropping the charge would feed the perception that famous people are treated differently.