There are different regulations concerning the school types. If Your child wants to attend a regular school in Thüringen (“Regelschule”), there are no special criteria. You can simple enrol Your child.
If You want Your child to attend a “Gymnasium”, there are certain criteria concerning the marks in the subjects German, Math, and “Heimat- und Sachkunde” that have to be met at the first Half of the 4th year of primary school. There is the possibility of a letter of recommendation, if the marks are not completely as required. If the marks are not as required and there in no letter of recommendation, the child hat to pass an exam. There are also criteria to change from the “Regelschule” to the “Gymnasium” after the classes 5,6 or 10. Please ask the local school authority for details.
For further information see:
http://apps.thueringen.de/de/publikationen/pic/pubdownload584.pdf
http://www.schulamt-suedthueringen.de/home/_data/Gestaltung_schulischer_Uebergaenge.pdf