The video showing Terry and Chauna Thompson restraining a man in a restaurant parking lot sparked outrage and protests in May 2017.
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.
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