A dispute over property left a 26-year-old Medford man seriously injured and a 21-year-old Smithtown woman under arrest after he jumped onto the hood of her moving car -- and fell off as she drove away, police said.

Suffolk County police said the incident occurred Monday in Medford. The man, identified as Daniel Keegan, was transported via Medford Ambulance to Brookhaven Memorial Hospital Medical Center in East Patchogue, police said.

Police said he was later transferred to Stony Brook University Hospital in critical condition with a head injury.

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The driver, identified as Kassandra Miller, left the scene and was later arrested, police said. She has been charged with leaving the scene of an incident without reporting, resulting in serious injury.

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She faces arraignment Tuesday in First District Court in Central Islip, police said.

Miller was driving a 1998 Toyota Camry on Race Avenue with Keegan "holding onto the hood" and said Keegan fell off, striking his head on the pavement, as she turned onto Newport Avenue, police said.

Additional details were not immediately available. Police only said the two were involved in a dispute that was not a domestic incident, but said the two were known to each other -- and had a "dispute over property."

It was not clear what type of property was involved.

Police are asking anyone with information to call Sixth Squad detectives at 631-854-8652 or Crime Stoppers at 1-800-220-TIPS. All calls will remain confidential.