This bug has been reported to Ant's original code as https://issues.apache.org/bugzilla/show_bug.cgi?id=42696 . It seems as if InflaterInputStream.close() didn't clean up the Inflater instance if one is passed in to the constructor. I'm currently testing the patch to Ant and will merge it over once I'm ready.
The code in Harmony does invoke inflater.end but calling it again won't hurt. OpenJDK's InflaterInputStream in fact behaves as described in Mounir's comment to Ant's Bugzilla.