Under what condition will the Supreme Court refuse jurisdiction for a state court decision?

The Supreme Court can refuse jurisdiction over a state court decision when there are adequate and independent nonfederal grounds to support that decision. This principle is significant because it respects the autonomy of state courts in interpreting their own laws and ensures that state judicial decisions can stand on their own merit when they are based on state law rather than federal constitutional issues.

In cases where a state court decision is premised on a state law that is sufficient to resolve the case independently of any federal law, the Supreme Court may opt not to intervene. This is particularly crucial when the state law provides a clear, adequate basis for the court's ruling, thus negating the need for federal oversight or review.

For instance, if a state court rules based on its interpretation of state statutes or common law without actually addressing constitutional issues, then the federal courts, including the Supreme Court, may decline to hear the case, even if it involves parties who might have a federal interest in the outcome.

While the other options discuss various aspects of jurisdiction, they do not evoke the same principle of state court independence that adequate and independent nonfederal grounds do, making this the correct rationale for the Supreme Court's decision to refuse jurisdiction.