I believe they should take a mental evaluation. I think this because if someone is going to be protecting its citizens then they should be able to protect us from themselves. If a "mentally insane" person ended up becoming a cop then that just creates dangerous problems for everyone. Its a good thing they do evaluate.
I attended about a week worth of the Iowa Police Academy, primarily for Iowa State Patrolman, but also utilized by sheriffs. While I am not a police officer, I was subject to mental test prior to being allowed to handle a firearm. The test consisted of 120 question that are worded in a way it is nearly impossible to cheat, and are analyzed by psychiatrists. My only concern was that it pretty basic. I'm not sure how effective this test was, but I feel like more could be done before we give people fast cars and handguns.
I hear stories of this all the time but cant find evidence of this being prevalent in culture. Cops shooting people, et cetera. I don't know. I really cant see why not other than expenses and the government being lazy, I don't think it will get passed. I cant decide.