Family members accompanied by a police officer left the property, showing obvious signs of distress.
Police will remain in place at the house overnight until a full scene examination can be completed in the morning.
They are treating the deaths as accidental. District Commander John Price said police believe that gas caused the deaths.
A car was believed to have been running in a garage with internal access to the house, he said - that door was open when police arrived at the scene.
A team of 30 staff are working on the investigation.
Ms George, who was born in the Cook Islands, moved to Ashburton about five years ago to work.
The Herald understands Ms George has close family in Australia who are making arrangements to get to Ashburton as soon as possible.
Maggie Toka was Ms George's best friend in the Cook Islands. The pair lived next door to each other.
Ms Toka now lives in Auckland. The pair had lost contact for many years but reconnected last year when Ms Toka heard Ms George had moved to New Zealand.
"She would have been 32 this year, we are the same age. She was my best friend at kindy and through primary school," Ms Toka said.
"I'm in tears and very shocked this has happened to my dear friend. We are having a class reunion at the end of the year where we were going to reunite with our old friends - she was supposed to be there..."
Ms Toka heard about her friend's death at 5pm yesterday. A relative of hers was in Christchurch for a wedding and had gone with others to visit Ms George.
"When they walked in they saw the body," she said.
"I was shocked when my brother texted me and said she'd passed away. I said 'no I don't believe it, it can't be'."
Ms Toka said Ms George had five children. Her three youngest lived with her and the other two were understood to be living in the Cook Islands with family.
"She came here for a better life for her children ... she loved it here. I tried to get her to come and live in Auckland but she always said no, she loved it down there (in Ashburton)."
"She was just so very funny, she was always making jokes," said Ms Toka.
"She was a very loving mother to her kids, a loving person. She like to make people laugh."
Tributes are flowing on social media from family and friends, many of whom heard the news of the deaths via social media.
"God please comfort my family for our loss. Fly high my aunty and three little cousins," Ms George's niece, Eireene Atingakua, wrote on Facebook.
She posted a photo of the family and was letting relatives and friends know the details of their deaths.
"Rest in loving peace my beautiful aunty Cindy George and our baby cousins. Unbelievable and shocking that yous (sic) have left us too early."
Alana Kavana said: "Rest In Peace Cindy and your adorable children. Definitely taken away too early but you are in the Lords arms now...Condolences to the family."
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The details so far
• A woman and three children were found dead in an Ashburton home
• The woman has been identified as Cindy George
• The three children have been identified as Pio Scarlet Jetejura Raukete, 5, Teuruaa Junior George, 3 and 2-year-old Telyzshaun Gordon Ricardo Nelder Kruz George
• Police believe the deaths were accidental
• A car was believed to have been running in the garage
• Police believe that gas caused the deaths
• Tributes are flowing in on social media from friends and family
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Ms George's friend Christine Isamaela said she was "so shocked" to hear the disturbing news.
"Not sure wat really happened they found Cindy & her kids dead... probably from some sort of gas leak," she wrote on Facebook.
"Just watching the news makes me cry."
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Tony Vainerere, the Pacific community liaison at Presbyterian support and leader of the Cook Island community, said he knew Ms George well.
"She was a nice person. She was bubbly and really outgoing.
"Last time I spoke to her was last Friday - I met her at the supermarket and we had a chat. She seemed well. It's so unfortunate this has happened. Very tragic."
Mr Vainerere said the deaths were very hard on the family and the "tight knit" community of Cook Islanders in Ashburton.
"But our people always come together at times like this," he said.
"It will be hard not to see her around town. We'll miss seeing the smiles on the children's faces - unfortunately we won't be seeing them again. It's very hard for the community to take."
Another friend said news of Ms George's death was hard to accept.
"I didn't wanna believe it coz I wanted to come & see you... RIP my dearest funny & loving friend Cindy George & your beautiful kids."
It is understood Ms George is separated from the children's father, who also lives and works in Ashburton.
- Additional reporting from the Ashburton Guardian