Sullivan was discharged from the hospital and arrested just after 4:50 p.m. Sunday, Kelley said.
According KSTU, Sullivan's son, who was born on Sept. 4 with no known health problems, was pronounced dead Sept. 17 by medical responders. Media reports say the boy suffered broken ribs, bruising and bleeding on the brain.
On the day of the child's death, Sullivan left the boy in the sole care of her 21-year-old boyfriend, Dylan James Kitzmiller, while she called a friend to discuss her desire to "get away from Kitzmiller's abuse." That same day, Sullivan said, she found Kitzmiller moving the child's legs in a rough, awkward way. Later that night, Sullivan heard the child making noises and gasping for air before he stopped breathing, KSTU reported.
Sullivan told police Kitzmiller abused the child and used heroin daily, KUTV reported.
Salt Lake County District Attorney Sim Gill said evidence showed Kitzmiller abused the boy and that Sullivan knew about it.
"There were statements that the child was being handled roughly by the arm and shoulder -- that Kitzmiller would throw the baby up in the air (and) catch him in the air," Gill said, according to KUTV. "The girlfriend indicated there was a level of abuse going on. She was aware of this abuse. She took no steps to stop this or to take the child to safety."
Sullivan is being held with no bond at the Cherokee County Adult Detention Center, Kelley said.
Kitzmiller was arrested Saturday on the same charges as Sullivan, according to reports.