A significant hurdle facing dyslexic children in New York was cleared on Wednesday, when Gov. Kathy Hochul signed a bill into law that requires private insurers to cover the costs of key diagnostic tests.

The bill, the first of its kind passed in the United States, is designed to increase early diagnoses of dyslexia and other learning differences, such as attention deficit hyperactivity disorder, or A.D.H.D.

Education leaders in New York have been slow to understand and adapt to dyslexia. Many students who struggle to read because of the condition are believed to have fallen through the cracks as the state has searched for ways to identify them and help them catch up.

As many as 10 to 20 percent of New York City students are estimated to be dyslexic, a share that Brad Hoylman-Sigal, the state senator who sponsored the bill, referred to as “daunting.”

Diagnostic tests, known as neuropsychological exams, can cost up to $10,000 and are required before parents can request services from schools, Mr. Hoylman-Sigal said. In some cases, children may go undiagnosed because of a lack of access to testing.

“Part of the problem is that most parents don’t have the resources to cover these exams,” he said. “It’s an ‘aha moment’ for so many parents understanding why their child may have been struggling in school.”

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The indictment comes five months after the couple was first accused of physically and emotionally abusing their daughter. The abuse occurred when she was 15 and 16 years old, prosecutors said in a news release.

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