For the entry with pets (cats, dogs, ferrets) from member states of the European Union there are no official requirements. The entry of pets from non-EU countries is regulated by EU Regulation No. 576/2013.
Please note that you are required to register the pet when importing or re-importing it from a non-EU country, so that a document check or identity check can be carried out.
If you enter the country with pets that do not comply with the applicable regulations, you must expect that the animals will be presented to the official veterinarian at the point of entry for a fee and the animal may then be sent back to the country of origin, quarantined for several months or, under certain circumstances, the animal may even be ordered to be put to sleep.
Detailed information can be found on the website of the Federal Ministry of Food and Agriculture