The British Transport Police (BTP) officers are accused of poking fun at 17-year-old Harvey Price in a video, the Mirror Online has revealed.
The teenager is autistic and partially sighted, and gains weight easily due to hunger-inducing Prader-Willi syndrome.
An investigation was launched at BTP’s Torphichen place station in Edinburgh after a whistleblower made a complaint to senior officers.
It is believed that senior officers seized at least one mobile phone and found a video in which a constable can be seen making the remarks.
Two other officers are accused of adding comments after the video was posted in a chat group.
The video was brought to the attention of senior staff by a colleague, who claimed racist slurs had been used.
All three officers have been served with disciplinary Regulation 15 notices and will face a hearing later in the year.
A BTP spokesman told the Mirror: “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 constable accused of making the remarks caught on video has been transferred to a station in north-east England, and may face criminal charges.
The other two officers 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.
Model and TV personality Price has previously spoken out about the level of online abuse or ‘trolling’ directed at Harvey, and in 2017 launched a petition for ‘Harvey’s Law’, to make online trolling a criminal offence.
She started the campaign after keeping a diary of jibes directed towards her eldest son only to be told by police that his online abusers could not be charged.
The British Transport Police Federation, which represents the officers, declined to comment to the Mirror.