Chauna and Terry Thompson have been charged with murder in the chokehold death of John Hernandez outside of a Denny's in Crosby in 2017.
Video shows the Thompsons restraining Hernandez in the restaurant parking lot.
Hernandez later died.
The medical examiner report states his death was due to a lack of oxygen in his brain.
In June, the Thompsons were indicted for murder. In July, Chauna Thompson was fired from the sheriff's office.
Now the Thompsons are asking for a change of venue for their trial, arguing there is prejudice against them.
The Thompsons also say investigators mishandled their case. Prosecutors deny those claims.
In court Tuesday, the Thompsons will have to convince the judge that they won't get a fair trial in Harris County.
The judge has already denied the defense's request to remove the district attorney from the case.
Their hearing is underway and will continue Tuesday.
The Thompsons are being tried separately starting in May.
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