Do I need to override GetHashCode() on reference types?

You only need to override GetHashCode() on reference types if you override Object.Equals().

The reason for this is simple - normally, 2 references will always be distinct (a.Equals(b)==false, unless they're the same object). The default implementation of GetHashCode() will provide 2 distinct hashes in this case, so all is good.

If you override Equals(), though, this behavior is not guaranteed. If two objects are equal (as per Equals()), you need to guarantee that they'll have the same hash code with GetHashCode, so you should override it.