The officer has been named by colleagues on social media as PC Mick Atkinson, a dog handler with neighbouring force North Yorkshire Police.
Memorial unveiled to North Yorkshire Police officer who died on duty in 1977A cause of death has not yet been given. He was found by officers from West Yorkshire Police at a house in Oulton, south Leeds.
PC Atkinson's Facebook page suggests he was the father of a baby daughter and was a passionate supporter of Leeds Rhinos and Leeds United.
North Yorkshire Police said:
"At 11am on Sunday morning officers from West Yorkshire Police were called to a household in their area in relation to a sudden death.
"Sadly, on arrival, officers found the body of a man, who was pronounced dead at the scene. A coroner’s inquest will be held, but police do not believe there are any suspicious circumstances surrounding his death.
"We can confirm that the man was a serving North Yorkshire Police officer."
Superintendent Mike Walker of North Yorkshire Police said:
“This is a utterly tragic incident. Our thoughts are with the officer’s family, friends and colleagues at this extremely difficult time.”
The force's chief constable Lisa Winward added:
“It was with great sadness that I learnt of PC Mick Atkinson’s sudden and tragic death this weekend.
“Mick was a distinguished officer and had been part of the North Yorkshire Police family for 17 years. He started his service as PC in Scarborough and then moved into the Dog Support Unit and became a handler. He was a well-liked and much respected member of the team and of our wider policing family and his loss will be felt profoundly.
“His death has come as a great shock to all of us and our thoughts are with his family, friends and colleagues at this extremely difficult time.”
Roads policing officer Sergeant Paul Cording said:
"Truly numb hearing the devastating news we have lost a friend and colleague over the weekend. I simply have no words and my thoughts are with family, friends and colleagues at this awful time."
Colleagues from the North Yorkshire Police dog section posted their own tribute on Twitter:
"Today we lost a colleague, but more importantly our friend and brother in blue! Take care and look out for each other! Rest easy big man.
"Aky was one in a million and will be missed by all! Everyone who met him has a great memory of him which shows how unique and special he is. Our love goes out to his family. We will miss him!"
Sergeant Andy Graham added:
"I will truly miss your sound no-nonsense advice, common sense and friendship. Rest easy brother."