As Shari pointed out, the tiles most likely might be of some asbestos mixture, but I would also add that any of the older paint inside the unit **could** also be lead based. Care should be used when stripping it as should care be used when removing the tiles.
At work they removed lead paints and asbestos (1920s through 1960s buildings). When they did it, they blocked off hallways at a time, enclosed all work areas, had masks, filters, positive air pressure, had special dumpsters and had outside air filter monitors.
Disturbed danerous materials (both known to the State of California, or not)

can pose certain health risks and at the very least some basic precautions should be taken when dealing with them.