Approached by The Yorkshire Post after a surprise appearance in Parliament today - as votes on Boris Johnson's Brexit deal are due to take place - Mr O'Mara refused to respond.
Mr O'Mara was asked why he had not been in Parliament since April, whether he was voting today, and whether he planned to return to Parliament or resign.
He was also asked whether he thought his constituents would be pleased he had travelled to Parliament today.
But Mr O'Mara repeatedly refused to answer and said he had been "hounded" by the press, before threatening to call the police if he was questioned further.
However, a man with him - believed to be his father - confirmed he would be voting before Mr O'Mara beckoned him away and told him not to speak.
Independent Mr O'Mara has not sat in Parliament since April and has had a difficult year which led to him announcing he would resign from the Commons in September, a plan he later postponed.
He has missed a number of the key votes on Brexit during 2019, including the vote in September which led to the so-called Benn Act, requiring the Prime Minister to seek a Brexit extension if faced with a No Deal situation.
In his constituency residents say he does not respond to emails, phone calls, or hold surgeries, resulting in the Liberal Democrat candidate Laura Gordon taking on casework.
There was surprise this morning when a photo of him travelling to London was taken by constituent David Cross.
Mr Cross told The Sheffield Star: "“It must be uncomfortable for him, to be honest, and he’s looking a little sheepish.
“I was very surprised to see him, given what a hard shift he’s put in this year.
“I’m a remainer but even if he votes against Brexit I can’t forgive him for anything.
“He’s an absolute disgrace. He should have done the decent thing and resigned so a by-election could be held.”
In July, Mr O'Mara announced he would step down after a series of problems which saw him suspended from the Parliamentary Labour Party and then resign from the party.
But the Treasury, which administers MP resignations, later announced that he had postponed this decision.
Mr O'Mara provided one of the shocks on the night in the 2017 general election when he ousted former deputy prime minister Sir Nick Clegg from his Sheffield Hallam seat.
But the new MP's political problems began a few months after his election when a series of sexist and homophobic online posts were uncovered which he had made when he was in his early 20s.
These included inviting the band Girls Aloud to an orgy and joking about the musician Jamie Cullum being "sodomised to death".
In December 2017, Mr O'Mara said he had scaled back his activities on the advice of doctors and later said he made three suicide attempts during his suspension.
Labour later said it had readmitted him but he then resigned from the party saying he had experienced "little to make me feel welcome, understood and accepted".
Describing himself as "the first autistic MP in our history", Mr O'Mara, who also has cerebral palsy, wrote: "I didn't commit any crimes, yet I have been made unfairly to feel like a criminal."Soon after this he again stepped back from his work in the Commons on doctors' advice.
In April this year, Mr O'Mara suspended case work in his constituency office for a month following reports all his staff had either been sacked or resigned.
In July, one of his staff, Gareth Arnold, used the MP's own Twitter account to resign in public and criticise his former boss.
Mr O'Mara responded with a lengthy statement, saying: "I will be taking time out to receive professional help to deal with my mental health and personal issues regarding self-medication."
Mr O'Mara used his statement to blame Labour leader Jeremy Corbyn for how he had been treated by the party.