(CNN) -- Three children and their mother who were found dead inside their partially burned house in southern Indiana had all been shot in the head, police said Saturday, with an internet rant tied to the woman drawing investigators' attention.
Results of a preliminary autopsy, conducted by the Kentucky Medical Examiner's Office, released Saturday revealed that Amanda Bennett, 30, had died from a gunshot wound to her head and smoke inhalation.
The same causes of death were listed for her 9-year-old daughter, Katelynn Bennett. Jasmine Abbott -- 14 and also Amanda's biological daughter -- was killed by a gunshot wound to the head, as was the woman's 4-year-old son, Ryan Bennett.
Shortly after 4:20 p.m. Friday, Austin, Indiana, police forced their way into the victims' residence after getting a request from a relative to check on them.
The police officer that went inside noticed that parts of the home had been burned and, after a "quick search," found the four bodies, according to a statement from Indiana State Police.
"This is a very, very tragic situation -- a very sad situation," Indiana State Police Sgt. Jerry Goodin said after the discovery, according to CNN affiliate WAVE.
Authorities subsequently opened what they're calling a "death investigation." They sent the bodies to Louisville, Kentucky, about 36 miles to the south, where the nearest medical examiner is located. They have not named any suspects in the killings.
"We have no reason to believe at this time that the public at large should be scared for their safety," Indiana State Police Sgt. Jerry Goodin told reporters Saturday.
Police are looking at an internet posting on the "Crothersville Forum," referring to a town near Austin, that mentions the late Amanda Bennett's husband by name. Two posts, both under the heading "Gone Forever," were published online Friday and contained urgent, heated language.
One of the posts reads, in part: "it's time to take the pain away ... you got what u wanted no wife an no kids."
Responding to a query about whether the post may have been written by Amanda Bennett, Goodin said state police detectives are aware of the post and other online posts that might be relevant to the case.
"That is something that has been brought to our attention -- absolutely, it has been," he said.
Deborah Davidson, who works at an elementary school that the two youngest victims attended, described Amanda Bennett as consistently friendly and warm, according to CNN affiliate WLKY.
TamRa Stidham, a high school classmate of Jasmine Abbott's, described Amanda Bennett as an unselfish mother, telling CNN affiliate WAVE, "Anything (her children) wanted, they got if she had the money."
Stidham said, too, that "everybody loved" Jasmine Abbott at Austin High School.
Meanwhile, friends and neighbors in the tight-knit community were distraught at the news.
"I was devastated, and I'm still devastated," Lula Davidson, who knew Amanda Bennett, told WAVE. "It wasn't meant for me to understand, but I would like to understand."