A troubled marriage, including a recent conversation about a possible separation, may have played a part when a retired police officer shot and killed two teenage daughters as they slept at their suburban home, then killed himself in the garage, police said Monday.

But there had been no threat or history of violence, no drug use or drinking, no health or psychiatric problems, leaving investigators with no satisfactory explanation for the startling crime.

"I'm not sure anybody can even understand how a person kills his children," Harrison police Chief Anthony Marraccini said.

A suicide note indicated the weekend killings by Glen Hochman, 52, of Harrison, a New York City suburb, were premeditated and the note gave some explanation, the chief said, but he would not elaborate. He said the note was probably written after Hochman shot the girls because, "he did indicate in the note that the two girls were taken away."

The note, a five- or six-page computer printout, was addressed to Hochman's wife, Anamarie, who was away with an older daughter on an overnight casino trip in Connecticut when the killings occurred sometime after 2 a.m. Saturday. The note bore no signature and was mostly taken up with "instructions on what Mrs. Hochman had to do to get things in order," Marraccini said.

The slain daughters, Alissa, 17, and Deanna, 13, were found in their beds, each from a single gunshot to the head, the chief said. Their father was also shot in the head, and the weapon, a .40-caliber Glock, was still in his hand, the chief said.

Hochman had recently retired after 22 years with the White Plains Police Department, but the Glock was not a service weapon.

Interviews with people who knew him, including former police colleagues, found no one had an inkling that "Mr. Hoffman would have committed this heinous crime," the chief said.

The father's body was found by Alissa's boyfriend. The boyfriend and the mother had become worried about getting no response at the house and she gave him a passcode to unlock the garage. He called police, who found the girls' bodies, Marraccini said. Three dogs also had been shot to death, probably after the girls, he said.

Marraccini said Glen and Anamarie Hochman had discussed a possible separation in mid-January. On Friday, the day before the shootings, she went to police to report an argument with her husband — over an $80 cellphone bill — because a friend had urged her to document such incidents, the chief said.

"She did not report any threat of physical violence," he said. "She didn't want us to pursue it, she just wanted to document it."

He said family strife "could have been a factor" in the killings.

Marraccini said the crime was "a difficult struggle for the family, for the police officers that were on the scene, for the community."

"It's difficult, especially when you see two young girls, their lives have been ripped away, brutally murdered," he said. "You can't get any rationale for that. I can't believe this man took his daughters' life. Even initially at the scene, we looked for other explanations, possibly because the act is so incredibly bad. But unfortunately, I haven't come up with any other explanation."