Deputy Chauna Thompson filed the suit in 2000 claiming that their child's emotional and physical well-being could be endangered if her husband Terry had full access and visitation.
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According to the suit, Chauna claims Terry routinely used illegal drugs and alcohol to an excess before the child was born and requested that he be tested for drugs and alcohol.
Chauna also claims that Terry was previously under the care of a psychiatrist and had demonstrated problems controlling his anger and temper. She requested that Terry be evaluated by a psychiatrist to determine whether he was suitable for access to the child, according to documents.
The couple is facing murder charges for the death of John Hernandez, a case that has been getting national attention.
Investigators said Hernandez and Terry got into an altercation outside a Denny's restaurant on May 28 in Sheldon, an unincorporated community in northeastern Harris County.
Surveillance video from inside the restaurant shows a scuffle outside and a man wearing an orange shirt taking another man down. He then holds him down for several minutes until authorities arrive.
Hernandez's wife said the fight began when her husband, who was drunk, went outside the restaurant to urinate and subsequently encountered Thompson.
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The two started fighting and Hernandez punched Thompson. Thompson then reportedly had him on the ground in a choke hold.
The Harris County Sheriff's Office confirmed that sometime during the fight Chauna, who was off duty, arrived to meet Terry. She noticed what was happening and tried to restrain Hernandez, witnesses said.
The couple then noticed he wasn't breathing and the off-duty deputy immediately began CPR and continued until EMS arrived.
Hernandez was left in a coma following the violent altercation, and he died days later after he was taken off of life support.
Forensics examiners have since ruled his death a homicide, saying he died from anoxic encephalopathy or lack of oxygen to the brain, due to strangulation with chest compression.
A week later, harrowing eyewitness video emerged that gave investigators - and the public - a closer view of the melee that eventually claimed Hernandez's life.
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New eyewitness video shows close view of deadly Denny's fight
After a day of testimony, the grand jury indicted both Thompsons for murder in the death of Hernandez on June 8. If convicted, they could each face five years to life.
Both Thompsons surrendered to authorities that evening and bonded out hours later.
On Tuesday, a judge set their bond conditions, ordering that the two have no guns, no contact with the Hernandez family and will undergo random urine tests while out on bond.
Meanwhile, the Hernandez family has filed a civil lawsuit against Chauna and Terry. They are asking for $1,000,000 in damages, hoping the money would help to take care of Hernandez's daughter.