[Here’s what you need to know about the measles outbreak.]

Under Arizona law, parents may decline vaccinations for their child based on personal, religious or medical exemptions. But that law is in opposition to the “parens patriae” theory, a centuries-old principle that empowers the state to look after the interests of children and others unable to care for themselves.

“It’s a pretty high standard to meet,” said Douglas S. Diekema, who has been a practicing emergency room doctor for 30 years at Seattle Children’s Hospital. “I don’t know that I’ve ever called Child Protective Services, though I’ve thought about it a couple of times.”

Police records show that on Feb. 25, Ms. Beck had taken her 2-year-old boy to a clinic, where his temperature was recorded at above 100 degrees.

The child’s doctor became concerned that he could have meningitis, after learning that he was lethargic and had not been vaccinated. Ms. Beck was told to take him to an emergency room.

“I called the doctor back and said ‘Hey, I’m not sure how you got this 105 reading, my son’s acting fine,’” Ms. Beck told a local TV station. “‘This doesn’t really seem like a medical emergency.’”

The child’s doctor, after learning that Ms. Beck had ignored the recommendation to take the child to the hospital and having follow-up phone calls to the family go unanswered, then contacted the Arizona Department of Child Safety.

Asked to do a welfare check, the police officers later arrived at the family’s door, but were not allowed in. The body camera footage released Thursday shows the police twice knocking and trying to enter, before an officer reaches Mr. Bryce by telephone just before midnight, and tells him that he needs to verify that their youngest child is improving.