"Neer" is a person's last name, a person who was involved in a case of child abuse.
"Neer states" is shorthand for: "the judge's decision in the case of Neer v (whoever) states that ..."
The decision that was finally reached (by the Supreme Court) in the case of Neer v. the State of Alabama was that "evidence regarding prior injuries to the child can be shown to the jury because it actually is relevant to deciding if a child's death was accidental."
So presumably there was a Mr. Neer who was convicted of abusing his child until she died. He appealed his conviction, claiming that the prosecution had made an illegal error when they showed the jury evidence of previous injuries to the child.
His case travels up the Courts of Appeal under the title "Neer v. (some agency or organization, such as a state or a District Attorney)" The v. part stands for "versus" but it's usually just pronounced "vee" in this case.
One of the most famous cases titled like that is Roe v. Wade (pronounced Row vee Wade) regarding abortion. The case is often referred to as "Roe," like this: "The political climate in the US may have changed since Roe, but many other factors have remained the same."
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