L.C.
At my local hospital/medical center, they have complimentary valet parking too. I tend to not tip, because there are signs displayed that tipping is not necessary.
I believe these valets are paid a living wage. They are necessary because the parking garage is pretty far from the hospital and medical buildings and gets full very quickly. It is extremely difficult for many people to walk the long distance from the parking lots to get to their medical treatment.
If you do want to tip them, $2 is probably appropriate.