If You Have Vermiculite Insulation...
You can assume that your vermiculite attic insulation has asbestos in it. Having it tested is very expensive, so the best thing to do in this situation is to leave the insulation alone.
Do anything you can to avoid disturbing the vermiculite and raising dust. Make limited trips to the attic.
If you have to go in the attic, take extra precautions to avoid disturbing the dust. Seal any cracks in the ceiling around light fixtures, any cracks that will allow vermiculite dust access to your home.
Check any HVAC (heating or air conditioning) unit located in the attic to be sure that it is not contributing to asbestos levels in your home.
Not a Do-it-Yourself Project
Seek a licensed, EPA-approved asbestos professional to remove any damaged vermiculite in your home. Inhalation of asbestos fibers has been linked to cancer.
A licensed, experienced professional will perform an air monitor test afterwards to ensure that there is no lingering air pollution as a result of removal.
Things You Can Do
Discontinue use of the attic as a storage space and take the extra step of wiping down the boxes you have used in storage. Use several wet cloths, do not reuse the cloths, and check local regulations for disposal of asbestos-contaminated items.
Wear protective clothing, gloves, eye protection, and a respirator. Remember, common dust masks are not effective against asbestos.