My wife has alleged that she made a police complaint against me in Germany for a false domestic violence case. Is there a way to find out if any complaint has truly been filed against me or not if I don't live in Germany anymore?
You can query the Zentrales Staatsanwaltliches Verfahrensregister regarding your own cases once they reach that level. I'm not sure how this works out if you are no longer in Germany, since you would have to prove that you are yourself. As I understand this site, they expect you to send a postal letter rather than a mail.
There is no guarantee of getting a complete answer. Investigations may be tagged as 'secret' to avoid warning the criminals. That would usually not be the case in a domestic violence investigation, but it is more common in organized crime cases and the like.
You can ask for a “Selbstauskunft”. I have no idea how you would get one, and what it costs, but the police would know. That would contain everything the police has on file about you (only you yourself would be able to get that information, everyone else would get something redacted).
If your wife’s complaint was serious enough to be written down it would be there. If she went to a police station, made a complaint, but let it slip to the officer that the complaint is false and only made to get you into trouble, then it might not ever have been recorded. That means legally the complaint doesn’t exist.