It is the responsibility of the class implementing the IDisposable interface to ensure that the method can be called multiple times without throwing exception.
To help ensure that resources are always cleaned up appropriately, a Dispose method should be callable multiple times without throwing an exception.
http://msdn.microsoft.com/en-us/library/fs2xkftw(v=vs.110).aspx
After an object is disposed, calls that fail because the object is disposed can and likely should throw an ObjectDisposedException (to aid in future debugging). If it is important that external objects know whether or not an object is disposed before making calls (because the object is shared), then it is customary to add a public boolean property (IsDisposed/Disposed) that indicates the state of the object.
EDIT: To more clearly cast this answer to the phrasing of the question, the class implementing IDisposable should implementing thread-safety if it is expected the class will be used in a cross-threaded environment. The link I posted shows an example of this at the bottom of the page.