Police were called to a ground floor flat on Falkner Street shortly before 19:30 BST.
A 30-year-old man was detained before being taken to hospital after falling ill.
Merseyside Police believe the incident is domestic related. They are not looking for anyone else.
The force added that a post mortem examination will be carried out to establish the causes of death.
As a precaution, and on advice from Merseyside Fire & Rescue Service following a report of a fuel leak inside the property, buildings on Falkner Street were evacuated.
Residents have been allowed back into their properties, with the exception of the properties either side of the address.
Detectives are appealing for anyone who may have information to contact them.

New Zealand-born Dale McIntosh, 47, of Pontypridd, admitted threatening behaviour at Llandudno Magistrates' Court.
The court heard he threw punches after being subjected to a "torrent of derogatory terms" while he was drinking in Rhyl on 4 February.
McIntosh apologised for his behaviour.
Diane Williams, prosecuting, said police outside a pub saw an "agitated" Merthyr RFC coach taking off his jacket before he cornered a man and allegedly struck him numerous times.
The former Cardiff Blues and Pontypridd RFC coach was arrested and told police he reacted after being taunted by a group.
Graham Parry, defending McIntosh, said it was a "very unfortunate incident" and his client was subject to a "considerable amount of very unpleasant provocation".
McIntosh apologised to the court for his actions, saying: "I'm not here to question it or make excuses for myself. I used physical force, I am a professional person and role model in my community.
"I extend my sincere apologies especially to the three arresting officers. Hopefully I will learn from this experience."

Phillip Chiyangwa, the chairman of Cosafa - the Council of Southern African Football Associations - has called for a meeting with other African FA chairmen in Harare in Zimbabwe on 24 February.
In a letter sent by Caf on behalf of president Issa Hayatou, the governing body tells Cosafa "you do not have any authority to convene such a meeting, without Caf knowledge nor without its required approval".
It adds: "Convening a meeting with representatives of many member associations outside Cosafa zone is deemed to represent an attempt to destabilise Caf.
"We draw your attention to the obligation of all zonal unions to respect the authority of Caf, and not to conduct in any activities that undermine the common objectives of Caf, for the benefit of African football development.
"The Caf Executive Committee reserves it rights to sanction any infringement to the Caf statutes."
Caf's warning comes shortly after Cosafa announced it had unanimously endorsed Ahmad Ahmad as a presidential candidate in upcoming Caf elections.
Ahmad, currently the head of Madagascar's FA, had already outlined his intention to challenge long-standing Caf leader Hayatou in March's elections in Ethiopia.
Hayatou is seeking an eight term in office.
Chiyangwa has already sent a reply to Caf's warning, writing "I was taken aback, to say the least, by the tone of your letter and the clear insinuation that such a gathering  between presidents of member associations on the African continent would be considered, outrightly, as an attempt to destabilise Caf".
He adds that Caf's statutes "promote friendly relations between National Associations, zonal unions, clubs, officials and players" and insists the meeting is for "that very objective".
Chiyangwa's letter also refers to Fifa's statues relating to the protecting of human rights which he says include "freedom of Association of member associations and zonal unions for the development and growth of the game on our continent".
A man has been arrested on suspicion of murder after the bodies of a woman and two children were found at a flat in the Toxteth area of Liverpool.
[NEXT_CONCEPT]
A former Wales rugby player-turned coach has been fined Â£350 for making threats after he retaliated to racist taunts while out in Denbighshire.
[NEXT_CONCEPT]
The Confederation of Africa Football has warned Cosafa over a planned meeting with other member associations which it says is "an attempt to destabilise" the governing body.