The only way to "tell" is to have samples of both the tile and its MASTIC (sometimes tile is asbestos free but mastic isn't) tested at an accredited laboratory. The first test will be a microscopic examination looking for the tell-tale signs of asbestos. Even if this examination does not find evidence (negative result) the false negatives are high from this, its a first step check to see if obviously positive for asbestos. If you get a negative result on both mastic and tile, the next step is a slightly more expensive test which actually "burns off" non-asbestos and the remaining is then tested using different equipment. A negative confirmation test sometimes discovers levels of asbestos that SHOULD usually be discovered in a microscopic examination but many factors can be missed, (like the particlar area not having a striated pattern concentration, the color of the tile, all kinds of issues that can provide a false negative. Sometimes the "burn" test yields percentage quantities that aren't usually detected by microscope, and a confirmatory negative is necessary before you can be reasonably assured it (tile AND mastic) is asbestos free.

A certified testing service that includes sample collection, should provide advice along with their reported results (in writing) regards to dealing with the situation should asbestos be found, regards to your "next step". Check out the HUD site and the EPA site for some more information regards to issues of asbestos flooring in home.

However its usually ASSUME asbestos regards to this situation until PROVEN otherwise.