The fire occurred around 1:30 p.m., according to the FDNY. About 12 units and 60 firefighters responded to the scene.
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A total of 20 people were injured, the FDNY said. Five refused medical attention, the other 15 were taken to the hospital to be checked out.
Five of the patients were inmates, the rest were staff members of the jail.
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The fire was placed under control less than an hour later around 2:15 p.m.
"The health and safety of those who work and live in our facilities is our main priority," said Deputy Commissioner for Public Information James Boyd. "We take arson very seriously and will pursue re-arrest of the individual involved pending the outcome of the investigation."
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The cause of the fire is under investigation.
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