Wells? Baths? Water channels? In the hospital? What are you, some kind of elf?
In my previous fort, due to a design flaw I had problems with siegers deciding to stand outside the cage trap passage leading into my fort to taunt me instead of charging into the cages. I suspect it was a pathing issue. I built battlements overlooking the entrance so I could have my xbow dorfs use them for target practice. Due to yet another design flaw, I had neglected the cliff face on the battlements' right flank into which I had cut the fort entrance. At the next siege, my archers lined up on the wall and were having fun with the first wave and a squad of gobbos from the far side of the map came down the cliff face. One of them was a crossbowman who started to use the rightmost dorf's back as a pincushion, that happened to be the squad's captain. Before I realized what was happening the captain was unconscious. After reloading, the rest of the squad finished off the gobbo on the cliff. The captain came to, went into a martial trance, emptied his quiver and passed out again. The rest of the squad broke the siege and once I lifted the alert someone dragged the captain off to the hospital where he spent over a month unconscious while waiting for his initial diagnosis. I kept checking up on him as he had six bolts stuck in him and was infected even before he went into his martial trance. After another month or so, I noted he still hadn't gotten his diagnosis (even though the CMD had no other labors assigned) and I was surprised to find him not in the hospital. I tracked him down hauling furniture or something, still infected, still with six bolts in him! So I turned off all his labors and hoped that things would get sorted out sooner or later. The next time I checked on him, he was in the hospital getting sutured. Later I found him wandering the halls, still infected, but now with six nice colorful sutures in him. Eventually, the infection cleared and I put him back onto full duty even though his wounds were still listed as yellow and I promoted him to militia commander.
I could be mistaken, but I don't think my fortress had any soap. I certainly didn't have a water source in the hospital.
Sadly, somehow the save file got corrupted and I had never made a back up.
The way I see it, any dorf who dies from an infected hangnail isn't even worth his weight in yak vomit.