I don't know if you will be successful in finding many established policies on this one.  You will no doubt come across institutions who have experienced either a request to film or have had a crew come in to film.

In most cases the request will be permitted or denied on a case by case basis relying on the reason or context for the film and the works of art that are intended for filming.  Culturally sensitive work or copyrighted work are mainly at risk.  If the filming is allowed under fair dealing then the previous concerns are not an issue. 

I hope this helps.
Helen Dunne
Museum Victoria, Melbourne, Australia