Asbestos in flooring was phased out starting in the 1970's. Until just recently, I think an outright ban did not exist.
If you are removing the flooring (tile squares?) I would wet the location before and during the demolition. Wear protective masks and gloves and hose off completely when finished. Seal all debris in plastic bags and get rid of them. Asbestos is only a problem when it is dry, disturbed and gets airborne.
I know tile and flooring guys who have worked with the stuff for decades and have no ill effects. Just be careful, not wildly paranoid.