John Hannigan, 48, was found unconscious in the property on Grosvenor Road in Rathmines on January 3.
He died in hospital seven weeks later.
Gardai said they are not revealing the findings of a post-mortem examination for “operational reasons”.
“Investigating gardai have not been able to determine the sole cause of John’s death as being due to natural or accidental circumstances and continue to investigate all the circumstances of this unexplained death,” said a Garda spokesman.
At around 1.30pm on the day he sustained the injuries, Mr Hannigan travelled to Balally in Sandyford to meet a family member.
Gardai have been unable to establish his movements upon leaving Sandyford up until the time he was found in the apartment block at 6.30pm.
They have urged anyone with any information to come forward.
