I would recommend they hire someone to research officers' everyday work and develop a fitness test that reflects what would generally be required in the course of their duty.

The main issue with generalized "fitness" tests is they'll use place-holder activities to try to gauge ability without recognizing that performance on those tasks may be influenced by factors other than what they're claiming to measure. Ex: arm/ab strength being equal, push-ups will be harder for females due to the different center of gravity/weight distribution. For similar reasons, it's easier to hip-throw/trip/unbalance a male if you're doing grappling/take-down exercises. A test where people have to carry a heavy pack puts females at a disadvantage, even with strength and endurance being equal, if the packs were designed with a male form in mind and the weight distribution and shape of the pack was not adjusted as needed. Etc. Ideally, you would have sets of tasks people could select from to show aptitude.