The dead body of a woman of about 30 and a man in serious condition were found in an apartment in the community of Motza near Jerusalem on Thursday.
The man was treated by a Magen David Adom team and quickly evacuated to the hospital in serious condition.
Paramedic Israel Weingarten said: "When we arrived at the house we saw a woman of about 30. She wasn't breathing and had no pulse and we were forced to declare her death. A barely conscious man of about 30 was also lying there. We administered life-saving medical care and evacuated him to the hospital in serious condition."
The police have launched an investigation and are examining the case as a suspected murder and attempted suicide.