GOLDEN, Colo. — Donald J. Trump has found a new reason to question the legitimacy of the 2016 election — ballots — and he wasted little time here on Saturday before taking issue with the voting system in this largely vote-by-mail state.

“I have real problems with ballots being sent,” Mr. Trump said, pantomiming a ballot collector sifting envelopes and tossing some over his shoulder while counting others.

“If you don’t have a ballot, they give you another one and they void your one at home,” he told the crowd at an afternoon rally, explaining how voters could go fill out their ballot at the back of the venue here. “And then, of course, the other side would send that one in too, but, you know, we don’t do that stuff. We don’t do that stuff.”