As the scene at O’Malley Park was still being preserved last night, gardaí have not been able to ascertain if it was a double murder or a murder/suicide.
The two dead people have been named locally as Des Kelly, 23, and Breda Waters, 28. Ms Waters was shot in the face.
It is understood Mr Kelly was in a relationship with another woman and had been attending a late- night party at the house in Southill where the bodies were found at around 11.30am yesterday.
The body of Ms Waters was found in an upstairs bedroom and the body of Mr Kelly was found near a back door downstairs.
A relative who was staying in the house with her baby raised the alarm.
Gardaí believe Mr Kelly was involved in a number of shootings in the city in the past week and was also jailed for his part in a fatal accident in 2008 in which a young girl was killed.
According to local sources, he was a member of a family linked to drugs-related crime in the Southill area and two of his brothers had died in tragic circumstances.
The latest deaths are not being linked to the feud which has broken out in the McCarthy-Dundon gang in the past week.
Southill parish priest Fr Pat Hogan learned of the news as he was preparing to celebrate Sunday Mass.
“It is very depressing that this is not the first family member to die. I knew brothers of this man, who are dead. They were very decent. Whatever happened here is absolutely shocking.”
Supt John Scanlon, who is leading the investigation, said: “Until we have completed a forensic examination we are keeping an open mind.”
State pathologist Dr Marie Cassidy will carry out postmortem examinations today.