SAN FRANCISCO — The California Supreme Court has ordered briefing on a legal question percolating in Contra Costa County, where attorneys are hotly debating whether prosecutors should run criminal checks on police witnesses.

It’s an issue that DA offices around the Bay Area handle differently, with a patchwork of policies on whether prosecutors have a duty to preemptively screen police as witnesses — just as they do civilian witnesses — and turn over any potential impeachment information to defendants.