Christopher Maynard, 46, also stole a laptop from the home of a dead man after being sent to guard his body.
In another offence Maynard cheated his own mother out of £13,000 after finding cash hidden in the loft of her home which had been saved by his late father.
A judge who jailed Maynard for four years, seven months, told him that he had brought shame upon himself and West Yorkshire Police.
Maynard was a north Leeds-based police constable at the time he committed the offences.
Connor Quinn, prosecuting, told Leeds Crown Court Maynard found £13,000 in old bank notes hidden in the loft of his mother’s home in 2009.
He took the cash to a bank and tried to pay the money into his own account but was refused.
Maynard was told he had to pay the money into his mother’s account.
He then duped his mother by claiming the sum paid to her belonged to him as it was part of a divorce settlement and she later transferred the money to him.
Maynard used the cash to buy himself a luxury BMW 3 Series.
The officer then targeted an 83-year-old woman after being sent to her home to investigate an allegation that a neighbour had been stealing from her.
Mr Quinn said that within weeks of meeting her she wrote him a cheque for £15,000.
The cheque was dated January 27, 2010 - the same day that the victim had been admitted to hospital suffering from chest pains and nausea.
The woman, who has since died, also gave Maynard a further cheque for £2,000 two months later.
Maynard then preyed on a 76-year-old woman in Rawdon after being sent to her home during another theft investigation.
The court heard Maynard developed a close relationship with the pensioner and would do shopping for her.
Mr Quinn said that the woman began to believe that she was his girlfriend.
Maynard took a total of £18,740 from her.
He was allowed access to her bank cards and was written cheques totalling £5,240.
Maynard also used her money to buy £9,000 worth of shares which are now worthless.
Mr Quinn read a victim statement to the court on behalf of the woman in which she stated: “I feel terrible. I feel he did an awful dirty trick on me and I feel upset.
“I couldn’t understand why he took all my money. I feel sick about what he has done.
“I thought we loved each other. He told me he loved me.
“I really don’t understand why he has done this to me because Chris was a police officer.
“I think he should go to prison for what he has done.”
Maynard stole a laptop from the home of a man who died in February 2012.
The officer volunteered to guard the corpse until the undertaker arrived at his home.
Maynard instead went searching in wardrobes among the dead man’s personal possessions.
The laptop was discovered at Maynard’s home when he was arrested when the other offences came to light.
Maynard, from Huddersfield, pleaded guilty to misconduct in a public office and two offences of theft.
The court heard some of the money he obtained was used to pay off gambling debts.
Paul Flemming, mitigating, described Maynard’s offending as the “single biggest misjudgement of his life.”
Mr Flemming said Maynard had now been sacked by West Yorkshire Police.
Jailing Maynard, judge Christopher Batty said: “You abused your position as a police officer in a calculated and deceptive way.
“You have brought shame upon yourself and shame upon the police force which you served.”
The judge added: “These are despicable offences, the grossest abuse of your privileged position.”