DEXTER — Police continued their investigation Tuesday to learn why a father fatally shot his estranged wife and two children before killing himself.

In the months before Steven Lake, 37, used a shotgun to kill Amy Lake, 38, and their two children, 12-year-old Monica and 13-year-old Coty, at their home in Dexter on Monday morning, he exhibited emotionally abusive behavior, according to court records.

Despite criminal charges against Lake for allegedly threatening his wife and children in June 2010 and a protection-from-abuse order served shortly thereafter, the court allowed Lake to have contact with his children.

A spokeswoman for the state Medical Examiner’s Office said Tuesday that Steven and Coty Lake died from gunshot wounds to the head. Amy and Monica Lake died from gunshots to the head and chest.

On Tuesday afternoon at the red house on Shore Road, near Lake Wassookeag, someone had placed a white cross with pink flowers next to the driveway.

Police continued to speak with the Lakes’ family members and friends and examine written and electronic records, said Steve McCausland, spokesman for the Maine State Police.

“We’re looking at the whole range of issues that have come up in the aftermath of this tragedy, but today is really an information-gathering day,” he said.

Investigators are looking into how Steven Lake entered the home and how he got a shotgun, McCausland said. He was prohibited by his bail conditions from being at Amy Lake’s home and from possessing a firearm.

Amy Lake, a teacher, did not call 911 on Monday morning. One of her co-workers at Ridge View Community School in Dexter called police after driving past the house and seeing Steven Lake’s Jeep in the driveway, police said.

Police later found a shotgun near the bodies. A flammable liquid had been spread inside the house, but it hadn’t been lit.

Steven Lake’s legal paper trail shows a history of emotional and verbal abuse toward his family.

On the night of June 14, 2010, Amy Lake told police that her husband had held a gun and talked about killing himself, the children and her while at their home in Wellington.

“While sitting on my bed with my children, my husband stood in the bedroom doorway with a loaded gun and started talking about hurting himself and/or myself and children. He was bringing up past verbal threats he has said to me and I felt they were all going to come true that night,” she wrote in her complaint, filed in Piscataquis County District Court.

When asked by police whether Steven Lake had a history of violence, she wrote, “not really, but a lot of emotional abuse.” When asked if he owned a gun, she wrote, “yes, but not currently in his possession.”

Steven Lake was charged with criminal threatening with a dangerous weapon and domestic violence criminal threatening; he was to go to trial next month.

Amy Lake filed for a protection-from-abuse order against him. His bail conditions on the criminal charges and the protection order prohibited Steven Lake from contact with his family, from going to their school or home, and from possessing a firearm.

About two months later, Steven Lake, through his attorney, Anthony Shusta II, requested that the court allow him to have contact with his children.

“It is anticipated that the minor children will be having contact with the defendant as recommended by their counselors,” Shusta wrote in court documents. “Said contact is recommended by the counselors and is in the minor children’s best interest.”

The request was not opposed by the state Department of Health and Human Services, Amy Lake or District Attorney R. Christopher Almy, and was granted in August. Steven Lake was still prohibited from contacting Amy Lake directly, going to her home or having a firearm.

About two months later, Amy Lake was shopping at the C&R General Store in Wellington. When she turned around, Steven Lake was behind her.

“I was parked right in front of the store, there was no way he did not know I was in there,” she wrote in a police report Nov. 11.

Steven Lake then drove past her house in Wellington, she told police. He later told his mother, who told Amy Lake, “Steven said that he wanted the meat grinder, the gun, safe and the weight bench” from their home, according to court documents.

Steven Lake was charged with violating conditions of release and violating a protective order. His right to see his children was revoked, according to bail conditions filed in Piscataquis County Superior Court.

Several months later, he again requested that he be allowed to see his children, if only through supervised visits. He submitted letters to the court from a licensed mental health and substance abuse agency in Newport, from which he had received services.

One counselor from the agency, Northeast Occupational Exchange, wrote: “I witnessed the emotion between the two of you when you met with your son in my office. I have learned nothing that would make me believe you would be a danger to your children. I see no reason why you should not be able to see your children.”

Another counselor wrote that Steven Lake had attended 18 of 21 group anger-management sessions and had completed all written assignments and participated in discussions.

The court granted the request and allowed Steven Lake supervised contact with his children.

The Lakes’ divorce process was continuing when Steven Lake killed his family Monday. The bank was trying to foreclose on their home in Wellington.

Skowhegan Savings Bank filed a foreclosure request in Piscataquis County District Court in May. At the time the Lakes were last notified that they needed to make payments on the five-acre property, they owed $80,755 in principal and $550 in interest, with interest accruing at a rate of $6.56 per day.

In court papers, Steven Lake is described as living in a camper in Mayfield Plantation and being self-employed by Lake’s Family Heating in Harmony.