Existing policies vary widely. Your situation seems to be one in which the photography is of a “commercial” nature, for which museums typically charge a substantial fee. Perhaps more important than fee structure is the fact that commercial photography typically involves equipment more elaborate and bulky than common handheld cameras — equipment whose setup and movement can put collections at risk — and whose very presence can interfere with or prevent enjoyment of your site by ordinary visitors. Camera crews, unless strictly monitored, are frequently inclined to re-arrange a setting to improve camera angles and image composition, and their personnel are seldom trained in the proper handling of collection artifacts. Intense lights that “bake” (and/or fade) collection items pose another predictable problem.
Be careful; insist upon insurance coverage (with your institution named as co-insured) adequate to cover any conceivable damage; have every action of the camera crew monitored by a staff member with supervisory authority.
If you care to contact me privately (email@example.com) I can steer you to a museum that hosts a great many still and video “shoots” and has developed policies and procedures that are about as close to “bulletproof” as you’re apt to find.
Alonzo Wood Homestead