Dan S
Edge of my lane as I am an interested observer with a cat bird seat re LEO hiring both local and Fed for the last 20+ years.
Sometimes it is a difference in degree as opposed to kind.
In good hiring times, if you are not a vet, having at least an associates degree was the floor in many departments, most of the time. Indeed, in my metro area, no promotion to SGT without at least an Asoc. No promotion to CAPT without a BA. In not so good times, "working toward it" or having a few steady years in a career field is enough.
In good hiring times, being a vet in lieu of college often meant looking at what branch and what you did. In not so good times, those with prior NON combat arms, MP, MI or IT exeperinece are often evaluated nearly as positively as those with----Vet=Vet, period.
I fully acknowledge there are exceptions to the rules I set forth above and policing (ergo hiring), to quote Pat Rogers (RIP) is very regional.
I will also say this, if you are interested in LE, ultimately get the BA even if you get hired without. Right, wrong or indifferent, the lack of a BA will be used against your career trajectory, for a variety of proper and/or less than proper reasons. Do not be low hanging fruit when you can help it.