As Republican candidate for president and later 45th President of the United States, Donald Trump has claimed repeatedly and vociferously that the 2016 General Election was tainted by massive voter fraud. Here we use aggregate election statistics to study Trump's claims and focus on non-citizen populations across the country, state-specific allegations directed at California, New Hampshire, and Virginia, and the timing of election results. Consistent with existing literature, we do not uncover any evidence supportive of Trump's assertions about systematic voter fraud in 2016. Our results imply neither that there was no fraud at all in the 2016 General Election nor that this election's administration was error-free. They do strongly suggest, however, that the expansive voter fraud concerns espoused by Donald Trump and those allied with him are not grounded in any observable features of the 2016 election.