Young said investigators found Gruodis had obvious wounds to her body that "lead us to believe it was a homicide."
Young would not describe the wounds, or say whether a weapon that might have caused the injuries was found inside the home at 7941 Chadbourne Drive, Unit B.
Gruodis' husband identified in court records as Peter Gruodis and her daughter, Airida Gruodis, who was at the home when police arrived, were in custody and being questioned, Young said.
Utah State Court records show the Gruodis family has a history of financial problems and domestic disputes, including instances of violence between Zita Gruodis and her daughter.
In 2010, a judge granted Zita Gruodis a protective order against her daughter, barring the younger woman from having any contact with her mother.
That orders appears to have been in place earlier this year and, in February, Salt Lake County prosecutors charged Airida Gruodis, 36, with a third-degree felony for violating the order, the records show.
Court records show a judge dismissed the no contact order at a 3rd District Court hearing in July.
The same judge later referred the case to mental health court at the request of defense attorneys in August, but the case lagged and records show Airida Gruodis was in the University of Utah's Neuropsychiatric Institute in early September. Another hearing in the case is set for December.
On Monday, Zita Gruodis was found in an upstairs bedroom of the Chadbourne home and investigators believe she may have been dead for some time, although no time line is yet clear, Young said. Police served a search warrant around 9 p.m. Monday and were expected to be collecting evidence from the home throughout the night.
Neither Gruodis' husband or daughter had been arrested Monday evening.
It's not clear whether all three members of the family had been living in the home. Court records also show that Zita Gruodis had filed for a divorce more than a decade ago, but the case was dismissed.
Cottonwood Heights police went to the Gruodis residence late Monday afternoon after a call from Unified Police, who responded to a traffic accident involving her husband at about 3:30 p.m. near 9400 South and 2700 East, Young said.
Young said a 911 caller contacted Unified Police to report a possible drunken driver in a white sport utility vehicle just after 3 p.m. Unified officers caught up to the car and watched the driver move erratically through traffic and then go off the road.
While talking to officers, Gruodis' husband said his wife "had just died and was dead at their home," Young said.
Unified Police then contacted Cottonwood Heights police to check the woman's welfare, and officers found her dead, he said.
"There are a lot of bizarre circumstances here," Young said.