Joe they do a multitude of mental health/psychiatric type tests including in person interviews with a mental health professional and written tests.  They've done so for years as I had to do them in the early/mid 90's when I became a cop.  They also talk to previous employers, friends, applicants former teachers, parents, etc.  Additionally they do polygraphs/voice stress analysis tests on each applicant.  It is incredibly in depth and many wash out.  Later in my cop career I was one of those people who were conducting the background checks and doing the voice stress tests.