Crawley is described as black, 5 feet 5 and 160 pounds with black hair and brown eyes.
Baby Noel is in foster care after spending 10 days in the neonatal intensive-care unit at St. Christopher's Hospital for Children.
Capt. John Darby, of the Special Victims Unit, said that after receiving tips leading them to about 10 women, police brought Crawley in for questioning Jan. 4.
At that time, Darby said, Crawley denied any relationship to the newborn. Police did not have enough evidence to arrest her, but did take the DNA sample that was eventually matched to the baby.
"We had her under our roof in here," Darby said. "There was an opportunity at that particular time to kind of straighten this out, to take possession of that baby and let us know. That didn't happen. Ultimately, and thankfully, we had the benefit of the science that did that for us."
DNA evidence showed that "she's 138.9 million times more likely to be the mother of that baby than if we just picked a random woman off the street," said Joseph Szarka, the lab manager from the Police Department's Forensic Sciences Bureau.
That match, coupled with information on the baby's grave condition provided to police by doctors who cared for her at St. Christopher's, was enough for the District Attorney's Office to approve an attempted-murder charge in the case, Darby said.
"As part of the charging process, doctors were consulted multiple times, and in fact this baby was very much in danger of dying out there, just before Christmas, in a box left on the street in cold temperatures," he said. "It doesn't get any worse than that."
He said that Crawley has at least one other child. Court records show that she has been arrested before on charges including assault and retail theft.
Besides the attempted-murder rap, Crawley faces charges of aggravated assault, reckless endangerment, endangering the welfare of a child and simple assault.
Anyone with information on Crawley's whereabouts should contact the Special Victims Unit at 215-685-3265 or 3251.