Authorities say the suspects dined at the Coram Diner on Middle Country Road last month and then dashed on their $80 bill.
After a female employee followed them outside and stood in front of their dark-colored four-door sedan, the suspects proceeded to hit the woman with the vehicle.
They then drove off with the waitress holding on to the hood for about 250 yards.
The victim suffered minor injuries after sliding off the car, which continued out of the parking lot.
Authorities believe the female suspect was driving at the time.
Anyone with information is asked to call Suffolk County CrimeStoppers and 1-800-220-TIPS to anonymously submit a tip.