Incidentally, no Stasi file for JC according to the German Archivist.
It would appear that, if there's nothing to hide, then he should hide nothing. Signing a release document would put the matter to bed one way or the other. That he seemingly refuses to do so indicates, to my mind at least, that he indeed has something to hide.
Besides, I presume that the Russians would have these archieves rather than the Czechs, given that post-68 the Czech intelligence community was, essentially, a branch office of the KGB.
Lastly, why do you mention Stasi? The accusation relates to Czech intelligence files, not German.