Since asbestos was once commonly used in construction as a fire retardant, there are still many homes that contain some asbestos. However, a visual inspection is usually not sufficient to determine if there is any asbestos in your home. If you suspect a fiber in your home may contain asbestos, you can call the National Institutes of Standards and Technology at (301) 975-4016; they will direct you to a lab that can test the fiber for you. Alternatively, contact a local construction professional.
As long as asbestos stays bonded to the other materials with which it is combined, it is not a problem to have in your home. But if the material it is bonded to begins to break apart, the asbestos fibers can be released into the air, becoming highly dangerous. If there is any crumbling insulation, patching or joint compounds in your ceiling, and your house is of a certain age, there is a risk of asbestos.
If you intend to do any repairs to your ceiling and suspect there might be chrysolite asbestos present, the short answer is, don't. This is potentially highly dangerous. There is no need to take this risk.
Instead, consult a professional contractor who is trained in asbestos removal. Each state has a licensing procedure to certify asbestos abatement (i.e. removal) contractors; make sure you find a contractor who has been certified in this area. Depending on how much asbestos is in your home, this process can cost anywhere from a few hundred dollars to around $20,000, and can require anything from a couple of hours to a few days.
Although it can be an expensive and inconvenient process, it must be undertaken by a professional; either ignoring the problem or attempting to handle it on your own can put you and your family at serious risk.