Suffolk Police were called to Wellington Court after a man was found with life-threatening injuries on Friday.
Officers were called to the address by the ambulance service at around 10pm on Friday.
The man, 36, was found in the bottom of a communal stairwell with life-threatening injuries. He remains in a critical condition in Addenbrookes Hospital, Cambridge, with injuries to his head.
Two men, aged 34 and 35 and both from Ipswich, were arrested on suspicion of assault GBH and taken to MArtlesham Police Investigation Centre for questioning.
They have since been bailed to return on Monday, September 28.
Anyone who witnessed the incident or who may have information is asked to call Ipswich CID on the 24-hour police number 101 quoting reference IC/15/3521.
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