Three people - believed to be a woman and two children - have been found dead at a house.
Just before noon, police were called to an address in Beeston Way, Allerton Bywater, after concerns were raised for the occupants.
Officers attended and three people were found dead inside the property.
A scene has been established and enquiries are ongoing into the circumstances.
Forensic teams are currently at the scene and part of the road has been cordoned off.
It is believed officers are hunting a man.
One woman, who lives on Warren House Road which backs on to Beeston Way, said: “We are just really shocked and sad.
“You just don’t know what’s happening on your doorstep.
“A couple lived in the house with two children - a boy aged about seven or eight and a girl aged 12 or 13.
“The kiddies used to play outside on their scooters.”
She added: “They kept themselves to themselves. I think they must have been here for about five years.
“I remember seeing them around for as long as I’ve lived here.”
She said she saw police arrive at the house at about 11.30am.
She said: “I’m absolutely shocked and really sad.”
Neighbours were in tears and visibly upset as they arrived home and were told by other residents about the news.
One man, who lives on neighbouring Davy Road just around the corner, said: “It’s a quiet estate.
“It’s got a good sense of community.
“There’s never really any anti-social behaviour or anything.
“It’s quite a middle-class area.
“Crime is relatively low there’s no bother.”
He added: “I’m shocked and saddened. I’m surprised and a bit confused about it all.”
Chloe Firth, 11, who is a friend of one of the children, said: “She was really bubbly and laughed a lot and was very kind to everyone else.
“I just can’t believe it. You don’t expect something like this to happen.”
Chloe’s father Sean, 44, added: “What can you say? It’s devastating.
“You don’t think anything like this could happen around here. It’s very quiet.
“People keep themselves to themselves.”
Mother-of-two Lesley Hirst, 47, of Beeston Way, said: “It’s just really sad, unexpected and a shock.
“It’s just a real family estate and it’s quiet. There’s an awful lot of children live on the estate.”
The property is in the new Millennium Village development at Allerton Bywater.
The Allerton Bywater Millennium Village, part of the Millennium Communities Programme, is a development of 520 homes including low cost housing as well as commercial and community space.
Allerton Bywater is built up of several smaller communities, mainly old mining villages such as Brigshaw, Hollinhurst and Bowers Row.