Usually they don't request for new police certificates. As long as you supply a recent one when applying (most suggest no older than 3 months), it's fine. They do a background check anyway.
By all means though, if you're sponsoring a family class member, get the medical before submiting the application. Even if the DMP tells you otherwise - I had to spend 2 weeks persuading the DMP in Slovenia that I have to take the medical before submiting and in the end they did it for me, but said "fine, but when they reject it, don't blame us!" xD