Shawn Peters, the author of three books on religion and the law, including “When Prayer Fails: Faith Healing, Children and the Law” (Oxford, 2007), said the outcome of the Neumann case was likely to set an important precedent.

“The laws around the country are pretty unsettled,” said Mr. Peters, who teaches religion at the University of Wisconsin Oshkosh and has been consulted by prosecutors and defense lawyers in the case.

In the last year, two other sets of parents, both in Oregon, were criminally charged because they had not sought medical care for their children on the ground that to do so would have violated their belief in faith healing. One couple were charged with manslaughter in the death of their 15-month-old daughter, who died of pneumonia last March. The other couple were charged with criminally negligent homicide in the death of their 16-year-old son, who died from complications of a urinary tract infection that was severely painful and easily treatable.

“Many types of abuses of children are motivated by rigid belief systems,” including severe corporal punishment, said Ms. Swan, a former Christian Scientist whose 16-month-old son, Matthew, died after she postponed taking him to a hospital for treatment of what proved to be meningitis. “We learned the hard way.”

All states give social service authorities the right to go into homes and petition for the removal of children, Ms. Swan said, but cases involving medical care often go unnoticed until too late. Parents who believe in faith healing, she said, may feel threatened by religious authorities who oppose medical treatment. Recalling her own experience, she said, “we knew that once we went to the doctor, we’d be cut off from God.”

The crux of the Neumanns’ case, Mr. Peters said, will be whether the parents could have known the seriousness of their daughter’s condition.

Image Leilani and Dale Neumann in court last spring in Wausau, Wis. Their case could create guidelines in an unsettled area of law. Credit... Rob Orcutt/Wassau Daily Herald, via Associated Press

Investigators said the Neumanns last took Kara to a doctor when she was 3. According to a police report, the girl had lost the strength to speak the day before she died. “Kara laid down and was unable to move her mouth,” the report said, “and merely made moaning noises and moved her eyes back and forth.”