How can I tell whether this roofing material is hazardous to tear down?
That looks like asbestos - the age would be about right. I'd get your local authority to have a look. They'll be able to advise on what you can and cannot do.

Asbestos is "safe" as long is at remains in one piece. It's the dust generated when it breaks up that's dangerous. If (and it's a very big if) you could remove it without it breaking then you'd be safe. However, that's unlikely to happen.

It will depend on your location but it can be expensive to have asbestos safely removed and the usual approach is to leave it in place if there's no danger of it breaking up.