I believe there are very few US Navy or Government owned museum ships in the US (Constitution, Nautilus, Cassin Young are the only ones I can think of) The vast majority that I am aware of are owned and operated by private entities. When ships are donated to museum efforts, they are actually donated and ownership is transferred to the recipient. Does the US Navy retain the right of repossession? Yes. Do they inspect the ships to ensure they are being taken care of? Yes. But the Navy no longer owns them and contributes Zero Dollars towards their operating costs and maintenance.
Do some state and local governments own or operate some museum ships?
Volunteer, USS Salem (CA 139)
United States Naval Shipbuilding Museum
Quincy, Massachusetts, USA