Now, they've identified the man they are looking for as 21-year-old Corey Brown.
He's a young man with a lengthy criminal history and two active restraining orders.
The shooting happened around 11:30 a.m. in the courtyard of the Lafayette Houses on DeKalb Avenue in Bedford-Stuyvesant.
Officers found 24-year-old Nicholeia Taylor with a gunshot wound to the chest. She was taken to Brooklyn Hospital, where she was pronounced dead on arrival.
Taylor, the mother of a 4-year-old boy who works with special needs children at night, was walking through the courtyard on her way to the gym when the gunfire erupted. At least five shots were fired.
The bullet casings were spread out, so the gunman was apparently moving as he was shooting.
Taylor's family is devastated and angry that this good mother and sister is suddenly gone.
"A hard-working mother, mother of one, goes to work every day, graduated school, college girl, got caught in the crossfire for a person that doesn't know how to aim, whoever he trying to shoot at," one relative said. "These little hooligans need to get a life, and I hope that they catch him and put him under the jail."
Brown is described as a black male approximately 5-foot-10 and weighing 180 pounds.
Detectives have gone door-to-door, but by late afternoon were still unable to make an arrest.
Wednesday, retired officers from the law enforcement alliance urged residents to come forward.
Neighbors say an arrest will ease their minds, but not completely.
After the murder of an innocent bystander in the middle of the day their sense of security will be shattered for a long time.
Anyone with information in regards to this homicide is asked to call the NYPD's Crime Stoppers Hotline at 800-577-TIPS.