Gardai are leading the investigation into the murder of Mary Ward in south Belfast earlier this month.
The mother-of-one was found dead in a house at Melrose Street, off the Lisburn Road, on October 1.
It is understood the young woman had suffered wounds to her neck.
A 26-year-old man, understood to be a foreign national, was arrested in Dublin on Wednesday and remained in custody on Thursday.
The 22-year-old was last seen alive on Wednesday September 25, throughout the day in Dungannon, Grand Central Bus Station in Belfast and Melrose Street.
Concerns have been raised after it emerged that in the weeks before her murder Ms Ward had reported to police that she was the victim of a violent crime.
The Police Ombudsman’s office is now investigating the PSNI’s response to that report.
Ms Ward is the fourth woman to be murdered in the north in the past six weeks.
The PSNI said on Thursday that that gardai are currently leading on what they described as a “joint investigation”.
Concerns about the police handling of Ms Ward’s case have emerged amid the ongoing controversy over the PSNI’s investigation into the murder of Katie Simpson four years ago.
Ms Simpson (21) died in hospital almost a week after an incident in Co Derry in August 2020.
Her murder was originally treated by police as suicide.
Jonathan Creswell, who was later accused of raping and killing her, took his own life on the second day of his trial in April.
Policing Board member Nuala McAllister has called on Chief Constable Jon Boutcher to meet with the oversight body.
”I am raising with the chair that this is a very serious incident, I have obviously been raising questions about Katie Simpson in the investigation for a long time,” she said.
A spokesman for the PSNI said: “The chief constable will provide an update at the next Policing Board meeting.”
The spokesman added: “This will be a joint investigation but with colleagues from An Garda Síochána currently leading on it and being supported by the Police Service of Northern Ireland, in accordance with provisions under the Criminal Law (Jurisdiction) Act 1976.”
