The lawsuit, filed in civil district court this week, accuses Glaxo of illegally marketing, pricing and promoting Avandia and violating Louisiana's consumer protection and unfair trade practices laws.
Caldwell claims Louisiana's Medicaid program paid more than $36 million in Avandia reimbursements that were based on fraudulent behavior. The lawsuit seeks financial penalties and repayment from Glaxo.
A spokeswoman for the company, Bernadette King, said Wednesday she was not familiar with the lawsuit and couldn't immediately comment. But she defended the medication.
"GlaxoSmithKline stands behind the safety and efficacy of Avandia when used appropriately and according to its label," King said in a statement.
The Food and Drug Administration has issued restrictions on use of Avandia because of its links to heart attack. The medication is under investigation by federal law enforcement officials and several state attorneys general.
Regulators in Europe pulled the drug off the market altogether.
Avandia was once one of Glaxo's top-selling products, but its popularity shrank since 2007 when its heart risks were first publicized.