The man is suspected in the deaths of the women whose bodies were found at a home in nearby North Royalton on Sunday.
Monday night, police responded to a home in Brunswick in search of Brinkman to question him about the triple slaying, reports CBS affiliate WOIO. Although he was "Facebook friends" with Suzanne Taylor, authorities are unsure how well the suspect knew the victim or her daughters.
He's accused of killing Suzanne Taylor, 45, and her daughters, Kylie Pifer, 18, and Taylor Pifer, 21.
Stark County Court records show Brinkman has been charged with two counts of murder. Police haven't said how they died. He says authorities are trying to figure out a connection between Brinkman and the mother and daughters.
Sheriff Maier said Mr. Brinkman worked for 71-year-old Rogell Eugene John and 64-year-old Roberta Ray John, whose bodies were found in their home in North Canton on Monday after their son grew concerned he couldn't reach them upon their return from a vacation.
The request was to determine if a vehicle reportedly driven by Brinkman, who was wanted for questioning in the North Canton deaths, was parked in a driveway at the Valley Forge Drive residence, where Brinkman had been staying for a few days.
No further details were available on the North Royalton case Tuesday afternoon.
Brinkman was thought to be an employee of a business owned by the Johns, but Maier said he did not have details about the business or how long Brinkman had been an employee.
Officers entered the home just before 5:30 a.m. the next morning and used a stun gun on Brinkman, who was holding a gun, Brunswick Lt. Robert Safran said. He had allegedly dated the daughter of the couple, his ex-girlfriend, and was allegedly watching their home while they were taking a vacation.
Brinkman was first arrested for receiving stolen property and unauthorized access of a computer system in Cuyahoga County, OH, in September 1998, according to the Daily Mail online.