If you had or suspect to have had relatives who were in the KPD, I have just updated the communist records page (which can be found by hovering over “Government Records” in the navigation) or by clicking here. While millions of communist-era records have been digitized in the Comintern project, aided by the archives in Moscow and the Library of Congress, personal files HAVE NOT been made available to the public. From my interactions with the Library of Congress, this seems to be due in part to the sheer volume of files that would need to be managed.
These records can be accessed through the archives in Moscow, however. If you find the name of a relative in the index of individuals, you can request to have this data transmitted to you electronically. For further information, please see the Communist Party Records page.