Two men forced their way into a flat and attacked another man in front of his mum.
The attackers threatened a 64-year-old woman and her son with a weapon.
The woman was not injured, but her 45-year-old son was seriously assaulted and suffered lacerations to his head.
He was taken to Glasgow Royal Infirmary where he was later released following treatment.
The attack took place in Burns Court, Kirkintilloch, on Thursday, April 3, at around 1.10am
Officers have been carrying out door-to-door enquiries in the area.
Detective Inspector Douglas Robertson said: “There doesn’t appear to be a motive for this attack, however we are following up a number of lines of enquiry.
“I am appealing to local people in the area who may have seen the two suspects around the time of the incident or who may have noticed something suspicious to get in touch with us, whatever information you have, it could prove vital to our investigation.”
Both suspects had their faces covered.
One is described as around 6ft 2ins tall, in his early 30s, with a heavy build.
The other man was younger and described as “podgy”.
Anyone with any information on the attack is asked to contact Kirkintilloch Police Office on 101 or Crimestoppers anonymously on 0800 555 111.