(CNN) A mother and her lawyers allege that ICE and those running an immigration facility in Texas provided substandard medical care for her toddler, who died six weeks after they were released.

Yazmin Juarez and Mariee were detained by ICE in March.

Yazmin Juarez, 20, and her 19-month-old daughter, Mariee, were detained at a facility in Dilley, Texas, "with unsafe conditions, neglectful medical care, and inadequate supervision," according to her law firm in a statement.

Shortly after they arrived at the South Texas Family Residential Center in March, Mariee contracted a respiratory infection that her lawyers at the firm of Arnold & Porter allege "went woefully under-treated for nearly a month."

Officials in Texas say they are investigating the case, and Immigrations and Customs Enforcement officials did not respond to specific allegations made by Juarez and her lawyers.

On Tuesday, her lawyers filed a notice of claim against the city of Eloy, Arizona, which is the prime contractor for the federal government in operating the Dilley facility. The claim seeks $40 million for wrongful death. CNN did not receive an immediate response from the city of Eloy to a request for comment on the case.

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