https://link.springer.com/article/10.1007/s00148-023-00953-1
"We exploit variations in the timing of decriminalization of same-sex sexual intercourse across US states to estimate the impact of these law changes on crime through difference-in-differences and event study models. We provide the first evidence that sodomy law repeals led to a decline in the number of arrests for disorderly conduct, prostitution, and other sex offenses. Moreover, in line with the hypothesis that sodomy law repeals enhanced mental health and lessened minority stress, we show that these repeals led to a reduction in arrests for drug and alcohol consumption."