Police said they immediately began a sexual assault investigation.
Though a woman in a vegetative state would still have a uterus that contracts, she would not be able to push and that could potentially lengthen labor.
The woman's mother, Katrina Cesena, told reporters she is sleeping in her daughter's hospital room until the perpetrator is found.
CNN said it is not reporting the woman's name because she is the victim of sexual abuse.
Detectives have asked men at the Hacienda HealthCare facility in Phoenix to give buccal swabs, Thompson said.
Sex abuse investigation underway after a patient in vegetative state for almost a decade gives birth.
To find the possible assailant, police in the south-western U.S. state are comparing DNA samples from the baby with male employees at the Hacienda Del Sol care centre, where the 29-year-old woman was a patient.
DRC police gather outside electoral commission
The mineral-rich country has never had a peaceful transition of power since it gained independence from Belgium in 1960. Candidates can appeal results if they wish and the final decision will be announced by the constitutional court.
Hacienda officials have called the situation "a deeply disturbing incident" and said they are cooperating with law enforcement and state agencies. She has been in the care of Hacienda HealthCare, a Phoenix-based nursing facility.
Local news website Azfamily.com first reported that the woman in a vegetative state for more than 10 years after a near-drowning had given birth. "None of the staff were aware that she was pregnant until she was pretty much, giving birth".
"I am deeply shocked and horrified at the treatment of one of our members".
Hacienda "will accept nothing less than a full accounting of this absolutely horrifying situation, an unprecedented case that has devastated everyone involved, from the victim and her family to Hacienda staff at every level of our organization", said Gary Orman, executive vice president of Hacienda HealthCare's board of directors.
'Sadly, one of her caretakers was not to be trusted and took advantage of her.
The woman's family "obviously is outraged, traumatized and in shock by the abuse and neglect of their daughter at Hacienda HealthCare", John Micheaels, an attorney representing the family, said in a statement emailed to media outlets after the DNA search warrant was confirmed. "It is my hope that justice will be served", the tribe chairman told CBS.
The Hacienda facility serves infants, children and young adults who are "medically fragile" or have developmental disabilities, according to the website.
The state's online complaint database for care facilities shows multiple complaints about the Hacienda center going back to 2013. But one complaint from December 2013 outlines an allegation that a staff member made inappropriate sexual comments about four patients two months earlier. That employee was later fired.
Jon Meyers, executive director of The Arc of Arizona, an advocacy group for people with intellectual and developmental disabilities, called the situation "disturbing, to put it mildly".
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