Plan on the application/hiring process taking 6-12 months to complete! After submitting a basic application for employment with the City, a brief review of your background is conducted and if selected, you will receive a notice of a date and time to take a written exam that assesses your reading comprehension. It is timed but not unmanageable. Brush up on vocabulary, analogies, etc. if you really want to excel. The bar doesn't seem to be set too high to "pass" the exam.
Following that assessment is a physical agility test. Google the "LawFit Challenge" to see what you're up against. The recruiter who sets your date and time for this test will provide you with the same background information...but it doesn't hurt to go on and begin getting in shape/ready for it. The most important thing is a timed mile and a half run. Different times are acceptable for different folks of different age groups, heights, weights, and gender. As a rule of thumb, if you can complete it in 12 minutes, you're looking pretty good. Don't worry, though. Some candidates move forward and take at least 20 minutes! (The entire assessment is scored on a points system. If running isn't your thing, you can make up the points somewhere else.)
A single bench press of your maximum weight is also a good way to score some points. Ideally, you should bench your body weight. You are given at least three attempts to reach your max. Most folks don't quite bench 100% of their weight. The most intimidating part of the assessment for the less strong applicants is jumping a five foot wall. Work on some pushups (not part of the assessment) and practice if you want to get over it. If not, make a couple of attempts and then just go around it. Your score is penalized but it's better than wasting a lot of time on a lost cause.
Providing you pass that assessment, get ready for a white glove check of your background (including a history of where you have lived, worked, and your credit). Honesty is the best policy...and a mandatory polygraph exam will likely identify any discrepancies. A one-on-one interview at your house (if you live in the area) is a part of this process! Clean up your mess and plug in some air fresheners.
A several hour long psychological exam is among the final stages of the application process and it's nothing to sweat. Just be ready to answer a ton of repetitive questions and have a brief conversation with a psychologist.
The pre-employment physical exam and drug screening are typically conducted after the "interview with the Chief" (aka: job offer).