They used credit cards stolen from an unlocked 2010 Mercedes-Benz to make purchases at stores in Deer Park, North Babylon, Bay Shore and East Islip last month, police said.
Now Suffolk County police are asking the public's help in identifying the man and woman shown on surveillance video at one of the stores where the purchases were made.
Police said the credit cards were stolen from the Mercedes parked outside Joe's Crab Shack at The Arches Circle in Deer Park on Oct. 18.
It was not immediately clear how many cards were taken -- or how many items were bought using the cards.
Police are asking anyone with information to call Suffolk Crime Stoppers at 800-220-TIPS. All calls will be kept confidential, and police said callers are eligible for a cash reward of up to $5,000 for information leading to an arrest in the case.