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Does it matter?

Another issue is that even if we had accurate statistics, they wouldn't necessarily support the argument. Donald Trump's rhetoric is meant to support increased spending on border enforcement. Deportees and many types of criminals can't enter the country legally with a visa. So they are more likely to cross into the US by crossing the border illegally. So even if illegal immigrants overall are less likely to commit crimes, people that would be stopped by increased border enforcement can still be more likely to commit crimes. And even that doesn't catch the full issue, as people who don't commit crimes could go through the legal immigration process. Making illegal crossings more difficult and legal crossings easier shifts more of those who would be law abiding from the illegal immigrant group to the legal immigrant group. So we could still have the good immigrants while reducing the bad.

Also note that criminals have more reason to cross the border multiple times. For example, Kate Steinle's killer has been deported five times. The typical illegal immigrant who avoids committing crimes while in the US gets deported less and therefore undertakes fewer crossings. So while criminals may not comprise a higher percentage of the immigrant population, they may still comprise a higher share of those making illegal border crossings.

Even if Trump's rhetoric is misleading, that doesn't mean that increased border enforcement wouldn't decrease crimes.