The “person of interest’’ in the murder of an Upper West Side ad exec is an emotionally disturbed 20-something woman who lived several floors from the victim for “many years” — and who had evidence of the slaying in her home, police and sources said Tuesday.

Cops executed a search warrant at the potential slay suspect’s apartment in the West End Avenue high-rise where 70-year-old Susan Trott’s body was found with her throat slit early Sunday “and recovered some items of evidence related to the homicide,’’ NYPD Chief of Detectives Dermot Shea told reporters.

“We believe the answers are within that building,” Shea said of the case.

“There is video surveillance in and out of that building. It’s still being reviewed,” he added.

The young woman is currently being “evaluated’’ in a local hospital, law-enforcement sources said.

“We have had prior contact with her,” a high-ranking police source said.

Still, it remained unclear whether the person of interest and Trott actually knew each other, Shea said.

“We have not had extensive conversations with the person of interest — but we will at some point,’’ he said.

Trott’s body was discovered during a wellness check by police after a worried business associate called the cops.

When officers got to Trott’s 14th-floor apartment, they found a blood-soaked pillow, a trail of blood leading to her bedroom and her corpse.

Linkedin user Judith Segaloff called Trott “my mentor, my rock and a kickass advertising pro’’ in a posting Tuesday.

“She was creative and eccentric and the last word was always hers,’’ the pal wrote. “She painted the world with big, bold, broad strokes and the universe was her canvas.”

But neighbors said some residents at the building near West 95th Street were not fans of how Trott would feed the pigeons outside.

“Some people didn’t like that because it attracts rats,” one local said.

An area maintenance worker who knew Trott added, “I would see her feeding the pigeons everywhere — in front of the building, at the corner. … We talked to her. We told her she can’t do that because it draws rats to the building.

“She just said, ‘OK,’ and she would go to the park to feed them.’’

When asked about complaints involving the victim’s pigeon-feeding, Shea said, “I do not have any information.

“I won’t speak to the motive,” he said.

Additional reporting by Georgett Roberts and Natalie Musumeci