I asked Tom about this last summer, and here is the conversation that ensued:

TL: Kreisler, yes, George Kreisler, his German name is Georg.  He is a
   Viennese artist who stole two of my songs.
ME: Like "Poisoning Pigeons In The Park"?
TL: Yeah, he has his own tune.  He doesn't use my tune.  It's not my song.
   There was nothing I could do about it, really.  I mean, what the heck.
ME: Is it the same words, do you know?
TL: The idea's the same.  I don't know German well enough to get it, but the
   idea's the same.  But it's a waltz; it's the same kind of song.  And in
   fact, when I got over there, they thought that I had stolen it from him,
   so I was able to, on my TV show there, which I did, I was able to get a
   dig at him, which was very nice.  Instead of yelling, instead of
   criticizing him, I said that I would like to thank George Kreisler for
   introducing my songs to the German public.
ME: HA HA.
TL: They all got it, because they thought that I had stolen from him.
   And the other one is "I Hold Your Hand In Mine", which is called "Die
   Hand" or "Der Hand", I forget which gender it is.  It's almost exactly
   the same, but the tune is quite different.   
ME: Oh really?  Interesting.
TL: So, there we are.  But there was nothing I could do about that, really,
   and I didn't care.
ME: When would that have been?
TL: That would've been...I don't think they put dates on records in those
   days...
ME: I know, it's really annoying they didn't.
TL: It would be certainly like late 50's.  Let's see, this one says...Vienna
   Midnight Cabaret with George Kreisler.  No, there's no date, but it's a
   10" LP, so therefore, it was some time ago.  He also stole a song from
   Eva Burrows, "The Girl With The Three Blue Eyes".  And...let's see if
   there's any date on the record here.  I don't see any.  So, who knows?
   Anyway, it was late 50's, my guess would be.  And he couldn't...it was
   before '59, as a matter of fact!  I mean, "The Hand" wasn't.  "Poisoning
   Pigeons" was before I had made MY recording, which was very strange to
   me.
ME: Ooh!
TL: So it must've been that he heard me do it in New York, or heard somebody
   describe it, or something, because it was definitely before I recorded
   it.  I had been performing it for years, but I had not recorded it.  So
   he got somebody...and the tune is, I mean, anybody could do it, if you
   got the idea and the waltz tune and all that.
   No, there's no date on this 10", which is the original one, Vienna
   Midnight Cabaret.  I asked if he was still alive, somebody, but nobody
   could find out.
   And the other one, the other one was a 12", and...anyway.  So that was,
   yeah, it would've been before '59, the Kreisler one, so...who knows?
   Anyway, next?
   When I find it, I'll...oh wait a minute, this looks familiar.  Yeah, here
   we are.  Die Georg Kreisler Platte.  No, there's still no date on it.
   Made in Austria.

Ich habe vor vielen Jahren im WDR eine uralte englischsprachige
Live-Aufnahme des Liedes gehört, gesungen von Georg Kreisler. Kreisler
hat (er lebte lange Jahre in den USA und trat dort in Clubs auf) Ende
der 40er /Anfang 50er Jahre in den USA zwei (englischsprachige) LPs
veröffentlicht, leider weiß ich nicht welche Lieder da drauf sind
(Vermutlich auch die von mir gehörte Aufnahme.  Kann da jemand helfen
und damit das Problem endgültig aus der Welt schaffen ? Sicherlich
jemand, der Zugang zum WDR-Archiv (in dem sowieso noch einige
Kreisler-Schätze ruhen...) hat). In seiner Autobiographie geht Kreisler
auch auf die Urheberschaftfrage ein (natürlich in seinem Sinne), einen
eindeutigen Beweis gibt er aber nicht. Meines Erachtens liegt also die
Lösung der ganzen Sache in den WDR-Archiven.

Also, wenn GK zum Beispiel geh'ma Hasen vergiften am Feld geschrieben hätte, und es ein Charleston, kein Walzer wäre, dann hätt ich eher dran glauben können, dass es Zufall war...

eine Best of Barabara Peters CD, dann muss die Versuchung schon sehr gross gewesen sein