This happens at the end of Goblet of Fire, after Harry has returned from the graveyard through the Portkey. Crouch Jr then takes him to his office and is about to kill him before Dumbledore intervenes. He then reveals his Dark Mark to which Dumbledore requests to see Harry's arm.
As said in the comments: this does not happen in the books, so we can only guess.
Dumbledore is kind of omniscient in the books and even more in the movies (as they are not able to describe in detail where he got all his knowledge from).
My best guess is, that Dumbledore most probably knows, what Voldemort needs to create a new body. He knows the formula and that it needs
Blood of the enemy forcibly taken.
Therefor he checks Harry for the existence of a wound that would show him, that his blood was taken.
Dumbledore furthermore reacts to what Crouch says:
BARTY JR *
I'll show you mine if you show me yours.
Barty Jr rolls up his sleeve to reveal a skull and snake marking.
DUMBLEDORE Your arm Harry.
BARTY JR You know what this means don't you? He's back. Lord Voldemort has returned.
So he suspects the wound to be on Harry's arm and finds it there. Barty draws the conclusion then...
*Both quotes taken from this movie transcript