The gear included a Taser, but the officer's firearm, badge and radio were not taken.
In addition to the puppy, jewelry and electronic items were also stolen.
Officials said all Durham Police Department employees are required to carry city-issued photo identification. Anyone unsure about an officer's identity should ask to see the officer's photo identification.
You can also call 911 to verify an officer's identity.
Anyone with information about the stolen items is asked to call Investigator J. Walsh at (919) 560-4582, ext. 29248 or CrimeStoppers at (919) 683-1200. CrimeStoppers pays cash rewards for information leading to arrests in felony cases and callers never have to identify themselves.