A detective constable failed to properly investigate child sex abuse claims and was only found out when the matter came to light again a year later.
Sussex Police officer Celia MacDonald decided no crime had been committed, did not record a crime or investigate further, the force said.
A gross misconduct panel ruled she would have been sacked if she had not retired just days before a gross misconduct hearing.
The 49-year-old, who was based in the Horsham safeguarding investigations unit, initially paid a visit with social services to the West Sussex family at the centre of the allegations, but took no further action.
A force spokesman said: "A year later, the same family came to notice again and the matter came to light, leading to an Independent Office for Police Conduct (IOPC) investigation into the officer's actions."
A man and a woman have since been arrested on suspicion of sexual assault on a child and have been released under investigation.
The panel, which conducted the hearing in her absence, found MacDonald would have been dismissed had she still been a serving police officer.
Detective Superintendent Steve Boniface, head of the force's professional standards department, said: "Protecting vulnerable people is a priority for Sussex Police, and while this was an unusual occurrence, it is still one that we take extremely seriously.
"We expect the highest possible standards of our officers and staff and where their conduct falls below these standards they will be robustly investigated.
"DC MacDonald's failure to perform her duty correctly potentially put vulnerable people at risk, although fortunately this case did come back to our notice and remains under investigation.
"The finding is supported by Sussex Police and highlights our determination not to bring into disrepute the enormous amount of good work carried out day-to-day by thousands of hard-working and enormously dedicated police officers and staff."
Investigations found MacDonald had a case to answer for gross misconduct, but a report has not been published due to the sensitive nature of the allegations, the IOPC said.
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