Dahlberg is accused of punching one man and pushing another, causing him to break his nose and cut his head when his face hit a pillar. One of his co-accused, Australian Nathan Miller, was sentenced on Monday to three weeks' jail after he admitted a charge of causing hurt.
Neither Singapore nor New Zealand police would comment on the hunt for Dahlberg.
Singapore has an extradition agreement with Commonwealth countries, including New Zealand, but Singapore Attorney-General Chambers' spokeswoman Jin Haw Li would not comment when asked if the office had made any requests for extradition.
New Zealand Ministry of Foreign Affairs and Trade spokesman Adham Crichton said the ministry did not comment on specific details related to extradition processes while an international criminal investigation may be ongoing.
"There was no request for consular assistance in relation to this case when it first came up so the ministry has not been involved."
Robert Dahlberg is the nephew of convicted murderer James Dahlberg, who was freed on Wednesday after spending 20 years in jail for killing his estranged wife, Ann Urquhart, in 1991. Urquhart's body was never found.