Presiding Judge Burlison’s most recent order (May 17) indicates that the City will remain operating at the Missouri Supreme Court’s Phase 0.
http://www.stlcitycircuitcourt.com/xml/judges/COVID-19%20-%20Administrative%20Order%2021.pdf
That means, in a nutshell, no in-person hearings unless absolutely necessary, and entry into the courthouse requires a court order and a mask.
That order will remain in effect indefinitely, and until the City has fourteen days of “improvement” in COVID-19 numbers. At that point, the Court can move up to Phase 1.