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The girl, identified in court papers as Cassandra C., learned that she had Hodgkin’s lymphoma in September. Ever since, she and her mother have been entangled in a legal battle with the state of Connecticut over whether Cassandra, who is still a minor, can refuse the chemotherapy that doctors say is likely to save her life. Without it, the girl’s doctors say, she will die.

“It’s poison,” Cassandra’s mother, Jackie Fortin, said of chemotherapy in an interview on Friday. “Does it kill the cancer? I guess they say it does kill the cancer. But it also kills everything else in your body.”

Doctors said in court documents that they had explained to Cassandra that while chemotherapy had side effects, serious risks were minimal.

On Thursday, Connecticut’s Supreme Court ruled that Cassandra had had the chance to show at trial that she was a “mature minor,” competent to make her own medical decisions, but had failed to do so. And so the chemotherapy treatments, which had already begun, will continue.

But the state said in court documents that Ms. Fortin had not brought her daughter to some medical appointments and was “not attending to Cassandra’s medical needs in a timely basis.”

The Department of Children and Families took temporary custody of the girl in late October 2014. Two weeks later, she was allowed to go home, so long as she underwent chemotherapy. But after two days of treatment, she ran away from home.

In a statement this week, the Department of Children and Families said it preferred to work with families, not compel them, but had no choice in some cases.

“When experts — such as the several physicians involved in this case — tell us with certainty that a child will die as a result of leaving a decision up to a parent,” the statement said, “then the Department has a responsibility to take action.”

Cassandra’s legal battle is not unprecedented, but it is unusual, said Dr. Paul S. Appelbaum, director of the Division of Law, Ethics, and Psychiatry at Columbia University College of Physicians & Surgeons.

But Ms. Fortin’s lawyer, James P. Sexton, said that Cassandra was only months shy of her 18th birthday, when the decision about her care would be hers to make. By then, the chemotherapy will most likely be over.

Today she is confined to the hospital. Her communications are limited, as are her visits with her mother. Mr. Sexton said the family would continue to fight in court.