It’s the same as in any larger city - crime does happen, but it tends to not be disruptive to the students here.
With city living, it is important to take steps to stay safe, and Yale invests in significant public safety resources which you can access.
There are certain areas of the city that one may feel less safe in than others but there’s really no reason to go into these areas for most people.
When the need is felt, Yale has safety services available such as safe rides, walking escorts and safety apps.
https://oiss.yale.edu/life-at-yale/safety-security, https://your.yale.edu/community/public-safety