Comparing crime rates between undocumented immigrants, legal immigrants, and native-born US citizens in Texas
https://www.pnas.org/doi/10.1073/pnas.2014704117
New Cato Research Shows That Illegal Immigrants Are Less Likely to Be Convicted of Murder in Texas
https://www.cato.org/blog/new-cato-research-shows-illegal-immigrants-are-less-likely-be-convicted-murder-texas
Immigrants Do Not Commit More Crimes in the US, Despite Fearmongering
https://www.americanimmigrationcouncil.org/blog/immigrants-do-not-commit-more-crimes-in-the-us-despite-fearmongering/
I selected three links, but Gemini provided more. Gemini has nearly always been right-on with topics that I'm knowledgeable in (mostly education), but as with any search or research, checking sources is vital.
Here's another study that I've found using traditional search:
THE INCARCERATION GAP BETWEEN IMMIGRANTS AND THE US-BORN, 18702020
We provide the first nationally representative long-run series (18702020) of incarceration rates
for immigrants and the US-born. As a group, immigrants have had lower incarceration rates than
the US-born for 150 years. Moreover, relative to the US-born, immigrants incarceration rates
have declined since 1960: immigrants today are 60% less likely to be incarcerated (30% relative
to US-born whites). This relative decline occurred among immigrants from all regions and cannot
be explained by changes in immigrants observable characteristics or immigration policy. Instead,
the decline is part of a broader divergence of outcomes between less-educated immigrants and
their US-born counterparts.
https://www.nber.org/system/files/working_papers/w31440/w31440.pdf