The order issued Monday marked the second unsuccessful attempt by Arias to seal her opening brief. A similar request was rejected in late May.
The latest ruling says Arias didn’t show that releasing the document would lead to a specific harm.
Arias is serving a life sentence for her conviction in the death of Travis Alexander.
Prosecutors say Arias attacked Alexander after he wanted to end their affair and planned a trip to Mexico with another woman.
Arias has acknowledged killing Alexander but claimed it was self-defense after he attacked her.
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