The investigation into the slaying of a 70-year-old woman on the Upper West Side is focusing on a female neighbor who lives in the victim’s building, the police said.

“We believe that all the pieces of that puzzle are in that building,” Dermot Shea, the chief of detectives for the New York Police Department, said Monday afternoon.

He did not identify the person the police want to question, but said she is a neighbor of the victim. Chief Shea said the police were investigating the nature of their relationship.

[Read more about the slaying.]

The announcement shocked residents along the quiet residential stretch of West End Avenue, who were still grappling with the grisly death of Susan Trott, a longtime copywriter who neighbors said lived alone.