The Corcoran Gallery of Art is taking steps to guarantee that most of its 17,000 artworks will remain in the Washington area and that the historic building near the White House always will display art, under the plan to turn over operations to George Washington University and the National Gallery of Art.

Legal papers filed by the Corcoran this week in D.C. Superior Court also show that the D.C. Attorney General’s Office is keeping a close watch over the dissolution of Washington’s oldest private art gallery and art college...