The state inmate population so far has not had any positive cases, she said.
But three flu cases are being treated in the infirmary on the Dayton prison grounds, and one person who tested positive for the flu is being treated at an outside hospital, Smith said.
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That person also has been tested for COVID-19 and the results are pending.
One housing unit at the Dayton prison is under quarantine in response to the flu cases, which is the standard practice, Smith said.
The corrections department is doing health screenings for essential staff and contractors before they enter prisons and other facilities.
So far, the department has not learned about any staff testing positive, Smith said.
All inmates entering prison are screened for COVID-19, and prison visits have been suspended to try to stop the spread of infection.
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