A spokeswoman for the state police, Sgt. Donna Tadiello, said the investigation will look at who purchased the revolver, how Denison obtained it and her history of mental illness.
"Everything about that weapon, we'll try to uncover as much information as possible," Tadiello said.
Police have not released the contents of the suicide note, and White said the family does not have any clues to what triggered the violence.
"Only God knows the answer to that," she said.
A community vigil is planned Friday night in North Stonington to support the boys' parents, who are described by friends in the rural southeastern Connecticut town as friendly and hard-working. Jeremy is a landscaper, but his work has been limited because of severe injuries sustained a year ago in a four-wheeler accident.
In Connecticut, those found not guilty of a felony by reason of insanity, or involuntarily committed to a psychiatric hospital, are prohibited from possessing guns. A person also must be deemed "suitable" by police before receiving a handgun permit, though there is no standard for determining suitability, said Mike Lawlor, the state's undersecretary for criminal justice policy and planning.
Connecticut also passed a law in 1999 that allows authorities to seize weapons from anyone if they have probable cause to believe the person poses a threat to themselves or others. That law was passed in response to the killing of four people at state lottery headquarters by an employee with a history of mental illness.
The law has been used more than 600 times, and with increased frequency since the massacre at the Sandy Hook Elementary School, Lawlor said.
"If you see something, you should say something to law enforcement, teachers or others in authority. And they, in turn, need to know this option is out there," Lawlor said.
State Senate Minority Leader John McKinney, a Republican, said he expects lawmakers will make some kind of recommendations concerning the possession of guns when someone in the home has mental health issues. But he said it will not be easy to choose an appropriate course.
"Some have suggested if there's someone in your household who is being treated for mental disorders, does that mean if you go see a therapist once? Just think of the examples. You're a child having trouble in school and your parents want you to go see a counselor, does that then mean the parents may not be able to own a gun or possess one?" McKinney said. "Those are very difficult issues."
Associated Press writers Susan Haigh, Dave Collins and Pat Eaton-Robb contributed to this report.