The U.S. Supreme Court's refusal to hear Arizona's appeal of a lower court ruling that overturned a convicted murderer's death sentence has opened the door for about 25 death row inmates to challenge their sentences.

The justices on Monday let stand the ruling that said Arizona unconstitutionally excluded evidence about James McKinney's troubled childhood and post-traumatic stress disorder that might have led to a lesser punishment.

The 9th U.S. Circuit Court of Appeals ruled last December that Arizona's causal nexus rule violated the Constitution. The rule required any mitigating evidence, such as mental illness or post-traumatic stress disorder, to be directly tied to the crime committed to be relevant in sentencing.