PC Mark Beardsley, from West Yorkshire Police was sacked from the force following a misconduct hearing earlier this month, which was held in private due to the nature of the allegations.
The hearing heard how PC Beardsley, who worked as a Safer Schools Officer, was told by a high school staff member that a child under 13 had been having sexual intercourse.
As a matter of law, such behaviour would amount in any event to the offence of rape of a child under 13 and would give rise to a significant safeguarding risk.
In a statement on its website, West Yorkshire Police said: "Even though PC Beardsley had been made aware of this information he responded inappropriately; he failed to record the matters disclosed as a crime;failed to initiate an investigation into suspected offences; and failed to make any referrals, record intelligence or take similar action for safeguarding purposes.
The misconduct panel were told how PC Beardsley discussed the matters further with the child and staff member in a second meeting at the school that took place a week later.
Following further evidence gathered in an investigation by the Independent Office for Police Conduct (IOPC), gross misconduct was proven against PC Beardsley and he was sacked immediately from the force.
Following the hearing, West Yorkshire Police said safeguarding of children is a key priority for the force.
“In this case Mark Beardsley was made aware of a serious safeguarding risk to a child at a school he worked at, but failed to either record or investigate the information he received, completely failing to safeguard a victim at risk of very serious harm.
“As a result the officer attended Misconduct Hearing where the decision of the independent legally qualified chair was to dismiss without notice.”