Sandra Bland, who was black, died in police custody three days after a physical confrontation with a white police officer during a traffic stop.
Police say that Sandra Bland hanged herself while being held in the Waller county jail. The family has denied that she was suicidal.
In the last 12 months, the death of black Americans in police custody has caused debate and protests.
An official post-mortem examination report found that Sandra Bland had hanged herself while in her cell.
The wrongful death lawsuit was announced in Houston by the family of the 28-year-old Chicago native.
In it, they name State Trooper Brian Encinia, the Texas Department of Public Safety in Waller County, the county’s sheriff’s department and two jailers as defendants.
The lawsuit seeks unspecified punitive damages “for egregious acts and omissions” and alleges Brian Encinia, 30, falsified an assault allegation to take Sandra Bland into custody.
The jail is accused of being “reckless” in disregarding her safety and failing to keep her free from harm.
Dash cam video shows Sandra Bland’s car being pulled over on 10 July for failing to signal during a lane change.
An argument began after Sandra Bland was asked to put out her cigarette and demanding she get out of her car.
Brian Encinia then points his stun gun at Sandra Bland, telling her “I will light you up” after she refuses his orders.
Sandra Bland was arrested for assaulting an officer. On July 13 she was found dead in her jail cell.
The Texas Department of Public Safety had previously said that Trooper Brian Encinia had acted improperly during the stop.
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