If the parent class uses Microsoft's IDisposable pattern, the child class should not override Dispose(void) but instead override Dispose(Boolean Disposing). If called with Disposing true, it should dispose the child class and call base.Dispose(True). If called with Disposing false, it should in most cases no nothing except call base.Dispose(False).
Note that in most cases, the call to base.Dispose(False) will do nothing, but it should be made anyway. If the child class would need to add additional "unmanaged resources" (i.e. if it has additional responsibilities that need to be performed in a finalizer) it should generally encapsulate those responsibilities into another object. Note that the question of whether a class has a finalizer is not just an "implementation detail"; adding a finalizer to a base class can be a breaking change, causing a program which would have leaked resources (bad, but perhaps survivable if it the program isn't run for too long at a time) into one which will, on random occasions, attempt to clean up resources which are still in use (won't often cause problems, but may cause rare but immediate failures).
IDisposable
then it should be disposed. – LukeH