Do physician assistants work in morgues?

Generally speaking - No. When a person is being taken to a morgue, they are already dead and have no need of a doctor. A mortician comes and takes the body to a funeral home for burial.

A Physician Assistant is like a "Junior Doctor" - They work under the supervision of physician. See: Physician assistants

Normally no, but of course I worked with a medical doctor who was driving a fork lift, so I guess they can work anywhere they want to.

But you have a mortician and a funeral director which are specific jobs which are either certified or licensed by most states.

Assuming you do not already have a degree as a PA and are wanting to work in a morgue, you can look into becoming an autopsy technician. Tech's are basically a PA for a pathologist- they perform the actual dissection and run the morgue while pathologists dissect the organs after removal and make the final call. I did this part time while I was in college as a pre-med. If you already have an undergraduate degree and especially if you already have a graduate degree (namely as a PA) you are probably overqualified since you do not need a degree to be an autopsy technician, just certifications and training.