I'm a police officer as well and when I took multiple pt tests for different departments I usually broke their mile and a half record in between the times of 7:30 and 7:50. It never moved the needle any faster and took me over a year and a half to land in a very well respected department. My advice is in terms working out is to stay well rounded. Pound the push ups, sit ups, and pull ups. They always felt my running was great but they wanted me much bigger.
The retired officers description is spot on. My advice also is to always display wonderful command presence and own a situation and scenario. Once on the streets use those command presence everyday by making sure your uniform is spot on and attitude is stern. A uniform that is right on always gives a good perception that you know your sh*t and your ready for a fight. Last thing, when in a situation always stick to your training. Never allow the media to dicate your decision making. They are fools and have no clue what they are talking about.