The two men and their service dog used an emergency slide to get out of an airplane preparing to fly from LaGuardia Airport on Monday morning.
The airline spokesman said passengers opened the door to a cabin activating the slide, and flew as a Delta flight bound for Atlanta, Ga.
WPIX-TV reported that the pair were detained by the Port Authority Police, but were not charged until Monday evening.
Brian Plummer, who was also on Flight 462, told The New York Times that he had seen the man, woman, and their pooch changing seats several times as the plane was preparing to depart.
Then, the man shot from his seat, telling a flight attendant that he could not sit down due to his post-traumatic stress disorder.
“If I sat down, I would freak out,” according to Plummer, the man said.
No one was injured in the incident.
The airline spokesman said that the plane, which was scheduled to take off before 10 am, returned to the gate, where the rest of the passengers were placed on other flights.
“Maintenance technicians have evaluated the aircraft and are scheduled to return to service this evening,” he added in a statement.