A Hofstra University student was driving drunk and without a driver’s license when her Jeep rear-ended a Nassau police car at the school’s entrance early Wednesday, officials said.

The two police officers in the patrol car when Katie Kirk, 21, struck it were taken to a hospital for neck and back injuries after the 3:45 a.m. collision on Oak Street, Nassau County police said.

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Kirk, of Bay Shore, was charged with two counts of DWI and unlicensed operator, police said. She was arraigned Wednesday in First District Court in Hempstead.

A spokeswoman for the Nassau police had no additional details about the officers’ injuries.

A Hofstra spokeswoman said Kirk is enrolled as a student at the university.

Kirk was released into the custody of the probation department, state court records showed.