Three British Transport Police officers are accused of making online jibes at the star’s eldest child and one may face criminal charges.
One of the men, a constable, has been placed on restricted duties while British Transport Police carry out a probe.
The force warned yesterday that the officer’s conduct could result in him facing criminal charges.
The investigation was launched at BTP’s Torphichen Place station, Edinburgh, when a whistleblower made a complaint to senior officers.
It’s claimed they seized at least one mobile phone and found a video in which an officer was filmed making the remarks.
His two colleagues have been accused of adding comments after the video was posted in a chat group.
All three have been served with disciplinary Regulation 15 notices and will face a hearing later in the year.
A force spokesman said: “We can confirm that a British Transport Police officer is under investigation in relation to allegations of gross misconduct and potential criminal offences.
“He is currently on restricted administrative duties.
“Two further officers are also under investigation following claims of misconduct. This inquiry is in its early stages and is being overseen by our professional standards department.”
The trio are also facing disciplinary proceedings over a series of other offensive communications which allegedly emerged after a phone was seized.
A source said: “This was brought to the attention of senior officers by a colleague who claimed racist terminologies had been used.
“A mobile phone was seized and the three officers will be up at a disciplinary hearing later in the year.”
Price’s son Harvey, 17, whose father is former footballer Dwight Yorke, has autism and is partially sighted.
He also gains weight easily due to Prader-Willi syndrome – a condition that makes sufferers constantly feel hungry.
The officer accused of mocking Harvey has been transferred to a station in north-east England.
The other two constables are also facing misconduct charges but remain on normal duties.
No date has been set for the disciplinary hearing.
The Independent Office for Police Conduct, which regulates the British Transport Police, has also been notified.
British Transport Police officers are responsible for policing the UK’s rail network.
Ex-glamour model Price launched a petition for Harvey’s Law in 2017 – to make online trolling a criminal offence.
The 41-year-old mum of five has also called for an official register of offenders after revealing her despair at the level of abuse aimed at Harvey.
She started the campaign after keeping a diary of the comments and taking them to police – only to be told that his tormentors could not be charged.
A spokesman for the Equality and Human Rights Commission said: “Online hate crime has risen dramatically and needs to be tackled and our hate crime laws need to keep pace with the rise of social media.”
A spokesman for anti-racism campaigners Hope not Hate added: “Abuse and intolerance of anyone for a disability or ethnicity is wrong.
“Those who serve to protect us from crime are rightly held to an even higher standard because of the trust we invest in them as public servants. Anything less is a derogation of that public trust, coming at a time when hate crimes have been rising.”
Price declined to comment.
The British Transport Police Federation, who represent the officers, declined to comment.