Of course they do.   

Almost every law enforcement agency is hurting badly for people.  When I interview people for my dept.  I want them to pass it, but I am also not just going to give them the job if they are going to be incompetent at it.

At my dept.  applicants are usually afforded the opportunity to tour the installations prior to going through the entire testing process.  We do this to "weed out" those who really have no idea what the job entails and only applied because they saw the add in the paper and we pay more than they are making now.   

The medical and psych are pretty expensive (about $1000.00 dollars at the dept I am at), so if you are at that point, they really wouldn't waste that kind of money on you unless they were really serious about hiring you.