Thomas Anthony Carlin, 43, maintains his innocence despite allegations of contempt of court during proceedings last week.
It is alleged he approached Lord Justice Gillen and threatened to arrest him.
He said on Monday he believed the judge was a "fugitive unlawfully at large".
Mr Carlin was told by Mr Justice Horner that he should "carefully consider his own position".
The judge said that Mr Carlin could face imprisonment if found guilty.
But Mr Justice Horner added that he was referring the case to the Attorney General for subsequent hearing.
Mr Carlin told the court "I believe there's no case to answer."
He demanded it be withdrawn.
The judge answered: "It's not going to be withdrawn."
The case of a serving PSNI officer accused of threatening to arrest a High Court judge has been referred to the Attorney General.