I've always wondered if there was, at some point, any direct (probably accidental) confrontation between soldiers of these countries with real casualties.
I was hoping someone would chime in with a better source but it looks like we are both out of luck, so here goes. This is from AC Brown's biography of Bill Donovan, so the book isn't about your question per se, but it does answer it indirectly. In the waning months of the European theatre of WWII the western allies were jockeying for position, especially in the Balkans, and shooting incidents were not uncommon nor were they accidental.
On page 641 Brown says "On April 2 1945 General Nathan N. Twinning, commanding general of the Mediterranean Allied Strategic Air Force and of the U.S. Fifteenth Air Force reported no fewer than six engagements with the Russians on that day, [including] 'Four Mustangs were attacked by between fifteen and twenty Russian LG-5s over western Austria. One Mustang was shot down, but the pilot was thought to be safe. Russian casualties, if any, were unknown.'"
I think there are other incidents in the book that take place on the ground rather than in the air but it's been a while since I read it, it's a big book, and it's not the best source for you anyway.