They say a Dunkin' Donuts worker saw John Greco's exposed genitals in the Feb. 27 stunt and then noted the make of his car and his license plate number.
Police say the 46-year-old Croton-on-Hudson resident was arrested last week and has been charged with misdemeanor public lewdness. He's due in court March 27.
Police released a statement Thursday saying it was "unknown how Mr. Greco took his coffee that day."
Greco says by telephone from his home that he has no comment on the police report.