The state attorney general is suing the company that provides health services to inmates at the Nassau County Jail.
Twelve inmates have died there since 2011 -- five in 2016 alone.
The lawsuit accuses Armor Correctional, which has an $11 million contract with the county, of "persistent illegal conduct" and "taxpayer fraud."
The attorney general says five of the 12 deaths resulted from "inadequate health care."
Armor Correctional says the allegation that it has not provided proper health care is "simply false."
The most recent inmate to die in custody was Emanuel McElveen, of Hempstead. His family says he died after being denied medical attention.
McElveen, who went by the name Manny, asked jail officials for medical treatment, but received a slow response, according to family members.
He died while hospitalized last week.