Nelms was one of three inmates who died in 2016 at the Bradley County jail.
The family is suing the county for failure to enforce official policies and customs.
They are also suing Bradley County Sheriff Eric Watson, saying he did not properly train correction officers or supervise the jail.
The family sued the correction officers; Gabriel Black, Ronald Reddish and Timothy Boyd for disregarding Nelms' medical needs. The three were indicted in December 2016 and charged with official misconduct.