How Processing Aufenthaltserlaubnis

A Führungszeugnis is a statement about any criminal record which should be issued by the police in the community where you are registered. I would ask the immigration office how long it usually takes and who you should contact for more specific information. Otherwise, just go to the local police and ask. Maybe if you live in a small community, the job will get done by the police in the nearest large city. Since you are from outside of Europe, it is possible that they contact officials in your home country. Such things can be very bureaucratic and take time.

Immigration office said they don't know long it takes.. l think it shouldn't be nessery  to contact officials in my home land, because l have lived in Germany since 4 years. I got an information that Landeskriminalamt in Stuttgart is incharge of issueing Führungszeugnis. I will contact them.
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I think it is if less than 5 years in any EU country they contact your homeland. That rule also applies to EU citizens.

It's always possible that people left their country to avoid punishment for a serious crime. Why should the authorities not check? For many countries they are denying entry under any circumstances for foreigners convicted of a serious crime even if they have done their jail time and regardless of how long ago it was..