Please review the Environmental Protection Agency's web site "Asbestos in Your Home."
Both the flooring and the adhesive could contain asbestos. I recommend you engage a locally licensed Asbestos Professional and obtain their recommendations for proceeding.
- Ask any asbestos professionals to document their completion of federal or state-approved training. Each person performing work in your home should provide proof of training and licensing in asbestos work, such as completion of EPA-approved training.
- State and local health departments or EPA regional offices may have listings of licensed professionals in your area.
In the meantime the EPA's web site cautions someone suspecting asbestos to "not dust, sweep, or vacuum debris that may contain asbestos. These steps will disturb tiny asbestos fibers and may release them into the air. Remove dust by wet mopping or with a special HEPA vacuum cleaner used by trained asbestos contractors".
For more information:
Read "What do I do if I think my linoleum might have asbestos?" a Q&A answered by Olga Alvarez.