It was around 9:40 a.m. Thursday when officers arrived at the home located on the 100 block of Cambridge Drive in the Windsor Hills community.
Investigators say a man came home and found his 61-year-old wife unresponsive.
The woman appeared to have been assaulted and was immediately tended to by arriving officers and paramedics at the scene. She was then transported by ambulance to the Christiana Hospital where she remains in critical condition.
Police are also looking for the woman's car - a dark gray 2010 Lexus HS 250 with Delaware tag 79381. Friday morning, authorities released an image of the vehicle hoping for leads.
At this time, investigators are not giving any information as to what happened inside the house, or how the 61-year-old was assaulted.
The incident was initially described as an apparent home invasion, but police say they are still trying to sort out exactly what happened.
Officers have been going door-to-door, talking to neighbors in the hopes of finding witnesses.
Anyone with information is asked to call New Castle County Police 302-395-8100.