The carjacking happened just before 5 p.m. last Tuesday.
The police report says a woman called 911 and said a man held her at gunpoint and tried to take her car while she was in it.
According to the report, she walked to her car, a Lexus convertible that was parked in level one of the garage, and put her luggage in the trunk and then got in her driver's seat. A few seconds later, her door reopened and she was staring at the end of a rifle.
The man eventually ran away without stealing the car.
Officials said a person was seen running away from Terminal 2 along John Brantley Boulevard at approximately 4:44 p.m.
The person was wearing a black hooded sweatshirt.
"RDU law enforcement would like to hear from anyone who was in or around the parking garage, exit plaza or traveling on John Brantley Boulevard when the carjacking was reported," said Chief Steele Myers of the RDU Airport Police Department. "They may be able to help us identify the person of interest or provide information that could be valuable to our investigation."
If you have any information, you are asked to call RDU's tip line at (919) 840-7573.