A baby at the centre of police inquiry remains critically ill.
A Fife street was cordoned off on Sunday after the five-month-old girl was rushed to hospital.
The girl was taken to the Royal Hospital for Sick Children in Edinburgh, where her distraught family were believed to be at her bedside.
Police Scotland confirmed that inquiries were continuing to establish the circumstances.
The occupant of one of two flats in Buckhaven’s West High Street cordoned off was named locally as Gordon McKay.
Neighbours said they saw a large number of police officers and forensics officers outside their homes on Sunday.
A woman who lives next to one of the cordoned off flats said she was shocked when the police knocked on her door on Sunday lunchtime.
She said: “They said they were concerned about a five-month-old bairn and they were asking for information.
“They kept asking me when I last saw the baby or heard her.
“The last time I saw her was Thursday.
“They wouldn’t tell me anything else and I didn’t know anything till I answered the door.”
The young woman, who asked not to be named, said there were around half a dozen CID and two uniformed officers outside.
“Since then there have been two houses with police outside them constantly,” she added.
“There were police with blue plastic on their shoes and gloves on in the flats.
“We’re not allowed to put anything in our bins and I’m having to sign in and out with the police.
“I’m not allowed any visitors at all.
“It’s quite worrying, especially because I don’t really know what’s happened.”
The woman’s sister told The Courier she had tried to visit her sister but had not been allowed beyond the cordon.
“I had to get a policeman to knock on her door and ask her to come out to speak to me in the street,” she said.
A spokesman for Police Scotland said: “Police in Fife were called to an address in West High Street, Buckhaven, around 12.30pm on Sunday following a report of concern for a child.
“A five-month-old girl was taken to the Sick Kids in Edinburgh where she remains in a critical condition.
“Inquiries are ongoing to establish the full circumstances.”