All of the victims were members of the same family, Cpl. Rhonda Fields said at a news conference Monday.
Consuelo Alejandra Haynie, 52, was found dead by officers Friday along with three of her children,15-year-old Alexis, 14-year-old Mathew and 12-year-old Maylan.
The children’s father, Colin Haynie, was the only survivor. He was released from the hospital Monday, Fields said.
Police are not releasing the name of the suspect because he is a juvenile, and Fields said they cannot give any details about how he is related to the victims.
The suspect, who has been charged with four counts of aggravated murder and one count of attempted aggravated murder, has refused to cooperate with investigators, Fields said.
The youth “surrendered peacefully, although he refused to speak with detectives,” Fields said.
Police are still trying to put together a timeline of events the day of the shooting. Police responded to a call about 7 p.m., Fields said.
Officials say the town of 11,000 people has been shaken by the killings.
“Our hearts go out to the families, loved ones and the close-knit neighborhood affected by this emotional, tragic incident,” said Grantsville Mayor Brent Marshall at the news conference. Counseling will be made available to the victims’ fellow students when school in Tooele County returns from the holiday Tuesday.
“There are a lot of ends to be tied up, there are a lot of questions that we would like to answer. Unfortunately there’s some questions we may never be able to answer,” Fields said, adding: “The biggest question that everybody has is: Why?”