PC Mick Atkinson, a dog handler with North Yorkshire Police, was discovered at a house in Oulton, Leeds, by officers from West Yorkshire Police.
North Yorkshire Police said PC Atkinson's collar number, 1066, was retired the following morning after his death.
Chief Constable Lisa Winward said: "Mick’s death this weekend has come as a great shock to all.
“As a mark of respect, his collar number, 1066, has been retired and will not be reissued to any other officer who joins North Yorkshire Police.
“We are all very touched by the kind words from members of the public and our thoughts remain with Mick’s family, friends and colleagues at this extremely difficult time.”
The officer had started his service as a Police Constable in Scarborough, before moving into the Dog Support Unit as a dog handler.
The circumstances of his death are not thought to be suspicious and the case has been passed to the coroner.
A Crowdfunding page to support people with mental health problems has been set up by friends of PC Atkinson.