IF asbestos is in this material it will be in the backing. As David suggests, it is not a health hazard in-place. During removal, the backing could become shredded and require a lot of scraping to fully remove. If kept wetted, no problem, if done dry, there will be some fiber release. Unlike asphalt floor tile, any fiber is not bound up in a plyable asphalt or vinyl matrix, but is in the backing. Only chrysotile asbestos was used in the backing material (relatively low health hazard) and you have about a 40% chance of it being there given the age of the material.
If you can pry up a small corner or cut a dime sized piece with a knife, that is all you need for a sample. Again the analysis is Polarized light microscopy (PLM). Our suggestions to install a floor over the top of the material means you don't have to worry about it. But then again, why not take an inexpensive sample so you know what to do.