PD Basti, a three-and-a-half-year-old German Shepherd, and his handler PC Adrian Firth, were helping firearms officers searching properties for suspects on Monday.
During the searches, PD Basti jumped through an open window onto a roof at a terraced property – and then slid down the tiled roof onto the floor below.
He was immediately taken from the scene to a nearby vets to be fully examined but did not suffer any injuries.
Nonetheless Basti is now taking time to rest and recuperate, the force said.
Temporary Inspector Pete Finch, of the armed response and dog support unit, said he knew the incident had attracted attention on social media, so wanted to assure people Basti was uninjured.
He said: “PD Basti was involved in a search with firearms officers when he unfortunately took a fall. We are all relieved he’s fit and well and are looking forward to him getting back to work after a short rest.
"The safety and wellbeing of our police dogs is paramount and they are a much-loved member of our firearms team.”
The incident happened where police were carrying out searches in Rushton Road, in Hanley.
The searches were taking place following an incident in Waterloo Road on May 9. A 35-year-old man from the local area has been arrested on suspicion of attempted murder and remains in custody. Enquiries are ongoing.