Study suggests ex-military cops are 2.9x more likely to be involved in a shooting if they had been deployed, and still 1.9x if they were ex-military but not deployed.
It's worth considering that people who leave the military to join another high risk of violence job may simply be violence seeking individuals, and that a randomly selected solider who was required to be a policeman would not show this effect. But given we can't really control that, we'd likely be better hiring fewer ex-military vets.
Another search suggests vets are over-represented in police jobs by about 3.5x their baseline rate