After an overnight standoff with Brunswick Police, Brinkman was taken into custody Tuesday morning.
"Most of it was done, face-to-face negotiations" through a window, Brunswick Police Lieutenant Robert Safran told the news station.
Police say a family friend found the three Sunday night at a home in North Royalton, south of Cleveland. A cause of death is expected to be released after an official autopsy is performed Tuesday.
Authorities say inmates killed two prison guards during a bus transport in Georgia and are now being sought by law enforcement.
Maier said police believe that the deaths of the mother and daughters in North Royalton happened before the Lake Township incident.
Plymale brought flowers to the house on Friday and left them for his girlfriend, Suzanne, around 4:30 p.m. because no one appeared to be home. Their bodies were cold to the touch - the North Royalton Fire Department arrived a few minutes later and verified the women were dead.
At around 8pm Sunday, Taylor Pifer's boyfriend entered the family's home, found at least one body and contacted Suzanne Taylor's boyfriend, who then called 911.
Maier said police do not think that the mother and daughters had any connection to the Johns.
Taylor Pifer attended Kent State University for study in fashion.
Police announced at a Tuesday news conference that an arrest warrant was taken out for Brinkman on two murder charges in the deaths of Rogell John, 71 and his 64-year-old wife, Roberta.
Court records show no violent history for Brinkman in either Stark or Cuyahoga counties.
George Brinkman Jr., 45, was arrested Tuesday after a standoff in Brunswick, and is a suspect in the killings.
Media and civilian bystanders gather outside the police blockade on Valley Forge Drive in Brunswick, Ohio. There had been a woman in the house, but she was released at some point during the siege.