The police collected the DNA of male employees of a private nursing home in Arizona this week as they broadened the investigation into allegations that a woman in a vegetative state there who gave birth to a child last month had been sexually assaulted.

On Wednesday, the Phoenix Police Department appealed to the community for information related to the case and said the investigation could evolve as detectives learn more about the circumstances of the woman’s pregnancy and the conception of the child.

“Right now we are investigating a sexual assault,” Sgt. Tommy Thompson, a police spokesman, said at a news conference. “Wherever this investigation takes us, we are prepared to go forward with it.”

The moves represented an escalation in the case, which on Monday prompted the resignation of the longtime chief executive of Hacienda HealthCare, the parent company of the nursing home. The police announced Friday that they had opened the investigation into the alleged assault.