If NASA’s scheme to snag an asteroid and move it into lunar orbit to be visited later by astronauts actually occurs, it will be the first time that a celestial object, however small, was moved from one orbit to another. The technical challenges will be daunting.
Space.com in an August 30, 2013 article suggests that there will also be legal challenges. “But does this bold plan run afoul of 1967's Outer Space Treaty (OST), which provides the basic framework of international space law, or 1972's Convention on International Liability for Damage Caused by Space Objects?”
Legal opinion suggests that in regards to the Outer Space Treaty, the matter will not arise unless and until two entities target the same asteroid for movement and/or mining. However there would be a question raised whether extracting valuable materials from an asteroid would constitute national appropriation which would imply a claim of sovereignty and therefore forbidden by treaty.
Clearly some kind of property rights convention needs to be negotiated, based perhaps on the principle that the first nation or company that takes control of an asteroid owns it. Someone really should write a book about all that.
As for who would be liable just in case a snagged asteroid should fall to Earth, that would apparently depend on fault, which is to say the question of what actions of the offending party led to the incident. That, of course, would depend on whether there are law courts not to mention people left after an asteroid crashes into the Earth.