German birth and baptismal records are not public records unless they are more than 110 years old. 20th C. vital records are kept at the Standesamt of the town and church records are kept at the church
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Births in Germany are registered in the Standesamt/Registry office in the town or district where a person was born. When you were born in Giessen, the Standesamt there should have your records. However, not everybody can request records. You will most likely need to prove who you are and that you request the records for yourself.You can begin a search in Giessen here: https://www.giessen.de/Rathaus/B%C3%BCrgerservice/
In addition, we located the page for requesting certificates from Giessen is here: https://translate.google.com/translate?hl=en&sl=de&u=https://www.giessen.de/%3Fobject%3Dtx%257C684.10089.1&prev=search&pto=aue
The web page is in German but you can translate the page by using the Choose a Language button in the upper right corner of the screen. You can also use Google.translate or similar programs that can assist you with a translation.
Since you are looking for baptismal records, you may need to look in the parish registers. Locating the correct church may become necessary. Familysearch.org has an information page that is helpful in locating church records from Germany. Please note that Familysearch.org only requires a Login and Password for use. For example you can access this page for different locations where baptismal records may exist in German cities/parishes Germany. https://www.familysearch.org/wiki/en/Germany_Church_Records#Locating_Church_Records
Good luck with your research!