This is what I read this weekend about that very thing, so I still have the link handy:
(Question)
How long does an infected corpse remain contagious?
(Answer)
A long time — although it’s still unknown exactly how long.
Remember, virus particles can last for days and even weeks in a drop of blood. So inside the entire body of the deceased patient, the virus can probably remain active for several months, Gonzalez says.
“That’s why it’s very important to [perform] the burial as soon as possible,” he adds. And to be extremely careful while doing it.
Not good. Not good at all, sigh.