The Hacienda statement said the company welcomed the move by the police and had looked into conducting its own DNA tests, but attorneys said it would be illegal.
A spokesman for Hacienda HealthCare says Bill Timmons announced his resignation Monday and it was unanimously accepted by the facility's board of directors.
A woman whose 22-year-old daughter is a patient at the facility said she refuses to leave her side until the investigation is conclusive.
Police in Phoenix are investigating reports of sexual assault, they confirmed.
Family members of other patients fear there may be more victims at Hacienda HealthCare, which has a history of patient mistreatment.
It would be the police who would lead DNA testing to figure out who fathered the baby, Solomon said, adding that it would be hard for Hacienda to escape liability. "And they didn't know what was wrong with her. ..."
The announcement came a day after the company's CEO resigned following reports that the woman, left in a persistent vegetative state for almost a decade after a near-drowning, had borne a child.
Police have declined to comment on the investigation. The source said that staff only found out she was pregnant on the day she gave birth.
In a statement, board member Gary Orman said Hacienda "will accept nothing less than a full accounting of this absolutely horrifying situation".
Karina Cesena says that her trust with Arizona's Hacienda Healthcare has "definitely been broken".
"This matter is now under investigation by the Phoenix Police Department", Sergeant Tommy Thompson told Reuters when asked about the media reports.
"We will do everything in our power to ensure the safety of every single one of our patients and our employees", Orman said.
Hacienda almost lost its Medicare funding in December 2013 after Arizona Department of Health Services (ADHS) found at least one staff member was abusive to multiple patients while several staff members were deficient in reporting patient allegations of abuse by staff.
Melissa Blasius-Nuanez with the Arizona Department of Health Services said in a statement that the agency is aware of the situation and is working with law enforcement in its criminal investigation.
Now, any male staff entering a female patient's room must be accompanied by a female staff member.