Take a sample in a plastic baggy to your local health department. They should be able to tell you if it is asbestos free or not, or tell you how to find out.
You didn't state your goal here, but I assume you want to get down to the original hardwood and resurface it. You didn't say if the adhesive was hard, or gummy, but you may find it is just easiest to remove the flooring and start over at the bare joists.
Without being able to see this first hand, it is hard for me to make specific suggestions.