Officials stressed she is not a suspect, but is just someone they want to speak to.
They are not releasing the name of the relative who made the 911 call, but said the caller was the only other person home at the time.
Kramer added that it's unclear whether that relative was in the same room as Clements or in another part of the house.
Wednesday morning, Hickenlooper ordered flags in the state lowered to half-staff between sunrise and sunset until after Clements' funeral. Arrangements are still being made.
The governor repeatedly praised Clements Wednesday afternoon, calling him a "dedicated, committed, funny, caring expert at corrections" who tried to ensure that prisoners had adequate support before their release.
"In many ways, Clements helped define what a public servant is," the governor said. "He did his job quietly and intently."
In addition to his wife, Clements leaves two daughters, Rachel and Sara, the governor's office said.
Clements' family released a statement through that office, thanking everyone for their support and concern.
"Our family has lost a devoted husband and a beloved father," it read.
"There are no words at this time to describe our grief and loss. We thank our friends and those praying for us here and across the nation. Your well-wishes and prayers bring us strength. We appreciate your continued respect for our privacy during this terrible loss."
Hickenlooper appointed Clements as chief of the state's prison system in January 2011, according to Clements' online state biography. Before that post, he worked for 31 years in the Missouri Department of Corrections.
From October 2007 until January 2011, Clements was the director of adult institutions for the department, the biography says, overseeing 21 adult prisons.