The video showing Terry and Chauna Thompson restraining a man in a restaurant parking lot sparked outrage and protests in May 2017.
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The victim, John Hernandez, later died after what happened outside the northeast Harris County restaurant.
In court on Monday, the couple asked to have the case moved out of the county, arguing there is a great prejudice against them.
Their attorneys argued officers also mishandled the case, but prosecutors denied those allegations.
Court convened this evening without a decision but will pick back up tomorrow.
Deadly Denny's chokehold fight saga: Everything you need to know
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A man who later died after a fight at a local Denny's was initially going to be charged.
What we know about the man and deputy indicted after deadly Denny's fight
A timeline: Deadly confrontation outside Denny's in Sheldon
Deputy Chauna Thompson and husband Terry out on bond after indictment
A deputy and her husband are due in court Tuesday on Murder charges.