In Germany today, a "Führungszeugnis" is a document which shows any criminal convictions you may have. Some jobs require that you produce a Führungszeugnis during the application process. If you have no record, it will state: "No entry."

The Nazis also required proof that you were "Aryan" for some jobs. This was done with the "Ariernachweis". So I assume your great-grandfather's Führungszeugnis is simply a record of criminal convictions (or lack thereof) and nothing especially ideology-related.

Can you post a scanned version with identifying data blacked out? I'd be happy to translate.

Edit: P.S. "Führer" means leader or guide, and Führung means "leadership" or "conduct", as in, how you conduct yourself. Just adding this to make sure people aren't confused as to why the famous f-word could still be used today on police documents. It's fairly mundane - for example, "Touristenführer" is tour guide, "Meinungsführer" is a leader of opinion, a "Tabellenführer" leads a league table in sports, a runaway train is "führungslos".