Detective Constable Stuart Galloway lied to the women, telling them that the man they claimed attacked them had been arrested and was going on trial.
The officer later convinced them that the man had admitted serious sex crimes – sparing them the ordeal of giving evidence.
He then fed them concocted stories about why the sentencing was put off on a number of dates, including that he had been arrested in London for speeding.
But Galloway – who had 19 years’ service – was rumbled when the youngest victim went to another officer asking for a crime reference number and claimed the 43-year-old had been investigating the case.
Yesterday the former officer, from Kilmarnock, Ayrshire, pled guilty at Glasgow Sheriff Court to wilfully neglecting and violating his duty. He resigned from Police Scotland in 2014.
The court was told that in November 2009, a 41-year-old woman – known as Witness A – reported that her father had abused her physically, mentally and sexually for years.
That inquiry was passed to the family protection unit and Detective Constable Carolanne Montgomery took statements from the witness.
Procurator fiscal depute Andrew Beadsworth said: “In her statement, the witness spoke about the male also raping and assaulting her mother, a woman aged 61, referred to as Witness B. On March 17, 2010, DC Montgomery obtained a statement from Witness A in relation to these allegations. A family protection unit file was raised in relation to Witness A and this file was allocated a reference number.”
The case was eventually allocated to Galloway, who had a meeting with both witnesses to update them about the progress and arrange to take further statements.
Mr Beadsworth said: “Stuart Galloway failed to detain or arrest the alleged perpetrator and he failed to report the case to the Crown Office and Procurator Fiscal Service.
“Galloway provided both witnesses with a series of false updates in relation to the results of his inquiries.”
Around September 2013, Witness A was told by Galloway that a trial for the alleged attacker was set for December of that year. Before then, he asked the mother and daughter to go to Pollok police office in Glasgow because he had “good news” about the offender admitting his guilt.
The pair were given sentencing dates but Galloway subsequently claimed they had been postponed, providing a variety of excuses.
When Witness B tried to get a crime reference number, Galloway told her nobody could find details because the case was sensitive and it could not be accessed.
After the final date for sentencing was cancelled, Witness A felt something was not right and discovered the truth.
Confronted about the matter, Galloway confessed: “I messed up.”
The man concerned was eventually convicted of historic domestic assault on Witness B and jailed for a year.
Sheriff John McCormick deferred sentence on Galloway until next month.