No, per square mile is meaningless.

Crime per square mile will be higher anywhere where people live in high rise buildings instead of suburbs.

So what? Is it worse that a robbery took place 15 floors below you rather than five blocks away? Because I don't see the difference at all.

If you're worried about personal safety, literally the only important denominator is per capita. That's the likelihood of something happening to you.

Per square mile has no relevance to personal safety. And if high population density is a factor in crime levels rising, that's already reflected in per-capita stats.