According to the church, Father Antonio Cisneros and another member of the parish staff both tested positive for coronavirus at St. Charles Borromeo on Tidwell.
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Cisneros last celebrated mass there this past Sunday at 6:30 p.m., the church said in a Facebook post.
He's been asymptomatic, but they are closing the church until further notice.
ABC13 visited St. Charles Borromeo March 15 as COVID-19 was starting to cancel churches and other events in the area, but they decided to stay open.
The diocese suggested Catholic churches do that because it would maintain some sense of normalcy.
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St. Charles Borromeo officials say they've taken the social distancing and sanitization guidelines very seriously.
The COVID-19 case count in Texas is rising dramatically.
Tuesday, Texas set a record for the highest daily total of new cases statewide at 5,000.
There have been more than 120,000 diagnosed cases in the state so far, and more than 47,000 are currently active.
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