Gardaí think the person believed to have stabbed a woman to death in an apartment in Limerick City acted alone.
A source familiar with the investigation said gardaí do not currently suspect that the person had assistance.
On Thursday, a 26-year-old man was arrested by police in Northern Ireland "on suspicion of murder". The man was held and questioned at Musgrave Police station in Belfast.
Detectives attached to Limerick’s Divisional Headquarters are believed to have travelled to the North to assist the Police Service of Northern Ireland (PSNI) in their investigation.
The victim, a woman aged in her 20s from Romania, was found with multiple stab wounds in an apartment on the Dock Road in Limerick City at around 1.30pm on Tuesday.
Romanian television reported the woman was a 27-year-old mother of four.
Senior garda sources said the joint investigation was at an “advanced stage” following the man’s arrest.
The sources said gardaí have contacted the victim’s family in Romania and a garda family liaison officer has been appointed.
Cross-border cooperation
In Limerick, gardaí have harvested CCTV from the Dock Road and O'Curry Street areas, in addition to other locations in the city.
The footage is being examined in an attempt to trace the movements of a man seen in the area between 1pm and 2pm on the day of the woman's death.
A senior garda source said cross-border legislation has allowed gardaí to "assist" the PSNI in the investigation.
Gardaí did not comment on whether a weapon has been recovered after teams combed a stretch of the Dock Road, O’Curry Street and Henry Street searching for evidence.
Forensic investigators have examined two locations - the apartment in which the woman's body was discovered and a nearby business premises.
Gardaí are appealing for anyone with information to contact Henry Street Garda station on 061-212400, the Garda Confidential Line on 1800-666 111, or any Garda station.