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Jermaine Crump, 36, is serving a life sentence in the shooting death of Crystal Crump in 2012.
Crystal was married to Crump's younger brother, and the couple and their two kids were living with Jermaine and his mother in Coffeeville.
Investigators say he chased the woman out of the home where they lived and shot her multiple times after she fell on the porch.
He claims he was acting in self-defense and thought she had a knife when he chased her out of the home.
The Mississippi Court of Appeals upheld his convicted last year, and the Mississippi Supreme Court denied a request to review the case Thursday.
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