Virts, 38, is charged with first-degree murder in connection with the death of Bobbie Jo Cortez, 36, found dead in her Ardee Way home in Dundalk last Thursday, police said.
"Police believe Virts killed Bobbie Jo [Cortez] on Wednesday, sometime before 6 p.m.," according to a statement from the Baltimore County Police Department.
Cortez was "all tied up, taped and [had] a sheet over her" when she was found by her daughter, Cayla, who was waiting to go to school on Thursday morning, the deceased woman's father told The Baltimore Sun.
Detectives think that Cayla Virts, twin sister Caitlyn Virts and a 13-year-old brother were home when their mother was killed, police said.
According to police, Timothy Virts left the Dundalk home with Caitlyn Virts sometime after 6 a.m. Thursday. Caitlyn was the daughter of Virts and Cortez, police said.
Police issued an Amber Alert for Caitlyn Virts Thursday and expanded the scope of the search to the national level on Friday.
Timothy and Caitlyn Virts were found Friday night after a hotel clerk in South Carolina called police when she recognized them from an Amber Alert post she saw on Facebook.
Caitlyn Virts was returned Saturday night to Maryland, where she was reunited with her siblings, all of whom are in the custody of social services officials, police said.
Homicide detectives flew to South Carolina after Timothy Virts was arrested there, and they continue to interview Virts, who agreed to talk to them, police said. Details of their conversations and 911 calls are being withheld due to the ongoing nature of the investigation, according to officials.
Although police initially said that extradition from South Carolina could take 7 to 12 days, police said Monday that Timothy Virts has waived extradition from South Carolina so Baltimore County and South Carolina authorities are working out logistics to arrange for his return to Maryland.
According to police, Caitlyn Virts appears to be physically unharmed and Baltimore County government will continue to provide all necessary resources to her and her siblings.