Victor Kennedy, who is serving a life term, fled while receiving treatment at Causeway Hospital in Coleraine late on Sunday night.
Officers, along with Rex the dog, began a hunt and inquiries led them to the town’s Ballysally Estate.
A PSNI Facebook post said the animal followed the trail across football pitches and through alleys, eventually finding Kennedy hiding behind bins in a resident’s back garden.
It added: “Determined not to return to prison the male resisted PD Rex, never one to shy away, he quickly detained the suspect taking the fight out of him in no time.”
The suspect was arrested and brought back to the hospital for treatment before being sent back behind bars.
The social media post added: “If it was not for Rex’s sharp nose and specialist skills this male would otherwise not have been located so quickly.
“PD Rex yet again displayed the importance of all the police dogs as an essential asset to the Police Service, and all it cost in the end was a play with a tennis ball.”
Kennedy is an inmate at Magilligan Prison.
He was imprisoned in 2009 for battering a Limavady schoolteacher to death.