Metro police said a man admitted to killing a woman during an argument inside his car earlier this month.
Stephanie Alexander's body was discovered in an alley between Fourth and Fifth avenues near Buchanan Street on the morning of September 5.
Police said Napoleon Harvey was taken into police custody the following day for a parole violation.
During an interview with detectives, Harvey admitted to killing the 39-year-old woman.
Police have yet to charge Harvey with Alexander's murder.
He was sentenced to 50 years in prison for robbery in 1983 and was paroled in 2006.
- Sept. 5, 2012: Woman's body found north of Nashville