Martin Cawley, aged 42, failed to attend an appointment on November 23, and there have been no confirmed sightings of him in the time since.
He was officially reported missing on December 6.
West Yorkshire Police said they were concerned for his welfare and is asking anyone who recognises him to get in touch.
Mr Cawley is white Irish, thin and 5ft 5ins, with short, grey hair, blue eyes and a ruddy complexion. He has a number of tattoos, including ‘Jordan’ on the centre of his neck, a black ink tomb on his left arm, an Irish flag with ‘Ireland’ on his left hand and a love heart scroll with ‘Ellie-Jo’ on his right hand.
He has connections to Ireland but is believed to still be in the UK.
PC Charlotte Smith, of Halifax Neighbourhood Patrol Team, said: “There have been a number of enquiries ongoing since Mr Cawley was reported missing last month but we are now seeking the public’s help in reporting any sightings of him or information about his whereabouts.
“He has been missing now for some time and we are concerned for his safety and welfare. I would urge anyone who can help our enquiries to please contact us via 101.
“Similarly, I would urge Mr Cawley himself to contact us to confirm he is safe and well.”