The complaint was made in relation to a post on November 9 on the case of a republican prisoner. The post has since been removed.
It was claimed the post related to the detention of a republican in March 2016 after his early release on licence was revoked by then secretary of state Theresa Villiers.
He had been sentenced to eighteen years in jail in 1994 for IRA activity and again for three years in 2011 for possession of a rifle.
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According to republicans he has been detained in Maghaberry prison for over two and a half years with no fresh charges put to him or trial held.
Police said in a statement: “As a Police Ombudsman’s investigation is ongoing it would be inappropriate for us to comment.”
The Police Ombudsman’s Office confirmed it was investigating a complaint.
In their original post PSNI Craigavon said prisoners are often released early and usually serve the rest of their sentence “on license” which means they have conditions they must adhere to. “If they breach those, they get taken back to prison for the remainder of the sentence.”
It is often peddled there was “no explanation” but all recalled prisoners get a full explanation, the post said. There is a simple alternative, the PSNI added: “Serve the sentence in full first time”.